---
_id: '21592'
abstract:
- lang: eng
text: We propose a reachability approach for infinite and finite horizon multi-objective
optimization problems for low-thrust spacecraft trajectory design. The main advantage
of the proposed method is that the Pareto front can be efficiently constructed
from the zero level set of the solution to a Hamilton-Jacobi-Bellman equation.
We demonstrate the proposed method by applying it to a low-thrust spacecraft trajectory
design problem. By deriving the analytic expression for the Hamiltonian and the
optimal control policy, we are able to efficiently compute the backward reachable
set and reconstruct the optimal trajectories. Furthermore, we show that any reconstructed
trajectory will be guaranteed to be weakly Pareto optimal. The proposed method
can be used as a benchmark for future research of applying reachability analysis
to low-thrust spacecraft trajectory design.
author:
- first_name: Nikolaus
full_name: Vertovec, Nikolaus
id: '87056'
last_name: Vertovec
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Kostas
full_name: Margellos, Kostas
last_name: Margellos
citation:
ama: 'Vertovec N, Ober-Blöbaum S, Margellos K. Multi-objective minimum time optimal
control for low-thrust trajectory design. In: ; :1975-1980.'
apa: Vertovec, N., Ober-Blöbaum, S., & Margellos, K. (n.d.). Multi-objective
minimum time optimal control for low-thrust trajectory design. 1975–1980.
bibtex: '@inproceedings{Vertovec_Ober-Blöbaum_Margellos, title={Multi-objective
minimum time optimal control for low-thrust trajectory design}, author={Vertovec,
Nikolaus and Ober-Blöbaum, Sina and Margellos, Kostas}, pages={1975–1980} }'
chicago: Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Multi-Objective
Minimum Time Optimal Control for Low-Thrust Trajectory Design,” 1975–80, n.d.
ieee: N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Multi-objective minimum time
optimal control for low-thrust trajectory design,” Rotterdam, the Netherlands,
pp. 1975–1980.
mla: Vertovec, Nikolaus, et al. Multi-Objective Minimum Time Optimal Control
for Low-Thrust Trajectory Design. pp. 1975–80.
short: 'N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: n.d., pp. 1975–1980.'
conference:
end_date: 2021-07-02
location: Rotterdam, the Netherlands
name: 2021 European Control Conference (ECC)
start_date: 2021-06-29
date_created: 2021-04-03T03:00:35Z
date_updated: 2023-11-29T10:26:49Z
department:
- _id: '636'
external_id:
arxiv:
- '2103.08813'
language:
- iso: eng
page: 1975-1980
publication_status: accepted
status: public
title: Multi-objective minimum time optimal control for low-thrust trajectory design
type: conference
user_id: '15694'
year: '2021'
...
---
_id: '29868'
author:
- first_name: F.
full_name: Jiménez, F.
last_name: Jiménez
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Jiménez F, Ober-Blöbaum S. Fractional Damping Through Restricted Calculus
of Variations. In: Nichtlineare Sci 31. Vol 46. J Nonlinear Sci . ; 2021.'
apa: Jiménez, F., & Ober-Blöbaum, S. (2021). Fractional Damping Through Restricted
Calculus of Variations. Nichtlineare Sci 31, 46.
bibtex: '@inproceedings{Jiménez_Ober-Blöbaum_2021, series={J Nonlinear Sci }, title={Fractional
Damping Through Restricted Calculus of Variations}, volume={46}, booktitle={Nichtlineare
Sci 31}, author={Jiménez, F. and Ober-Blöbaum, Sina}, year={2021}, collection={J
Nonlinear Sci } }'
chicago: Jiménez, F., and Sina Ober-Blöbaum. “Fractional Damping Through Restricted
Calculus of Variations.” In Nichtlineare Sci 31, Vol. 46. J Nonlinear Sci
, 2021.
ieee: F. Jiménez and S. Ober-Blöbaum, “Fractional Damping Through Restricted Calculus
of Variations,” in Nichtlineare Sci 31, 2021, vol. 46.
mla: Jiménez, F., and Sina Ober-Blöbaum. “Fractional Damping Through Restricted
Calculus of Variations.” Nichtlineare Sci 31, vol. 46, 2021.
short: 'F. Jiménez, S. Ober-Blöbaum, in: Nichtlineare Sci 31, 2021.'
date_created: 2022-02-17T07:28:47Z
date_updated: 2023-11-29T10:23:46Z
department:
- _id: '636'
intvolume: ' 46'
language:
- iso: eng
publication: Nichtlineare Sci 31
series_title: 'J Nonlinear Sci '
status: public
title: Fractional Damping Through Restricted Calculus of Variations
type: conference
user_id: '15694'
volume: 46
year: '2021'
...
---
_id: '19938'
abstract:
- lang: eng
text: 'We show that symplectic integrators preserve bifurcations of Hamiltonian
boundary value problems and that nonsymplectic integrators do not. We provide
a universal description of the breaking of umbilic bifurcations by nonysmplectic
integrators. We discover extra structure induced from certain types of boundary
value problems, including classical Dirichlet problems, that is useful to locate
bifurcations. Geodesics connecting two points are an example of a Hamiltonian
boundary value problem, and we introduce the jet-RATTLE method, a symplectic integrator
that easily computes geodesics and their bifurcations. Finally, we study the periodic
pitchfork bifurcation, a codimension-1 bifurcation arising in integrable Hamiltonian
systems. It is not preserved by either symplectic on nonsymplectic integrators,
but in some circumstances symplecticity greatly reduces the error. '
article_type: original
author:
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
citation:
ama: McLachlan RI, Offen C. Preservation of Bifurcations of Hamiltonian Boundary
Value Problems Under Discretisation. Foundations of Computational Mathematics.
2020;20(6):1363-1400. doi:10.1007/s10208-020-09454-z
apa: McLachlan, R. I., & Offen, C. (2020). Preservation of Bifurcations of Hamiltonian
Boundary Value Problems Under Discretisation. Foundations of Computational
Mathematics, 20(6), 1363–1400. https://doi.org/10.1007/s10208-020-09454-z
bibtex: '@article{McLachlan_Offen_2020, title={Preservation of Bifurcations of Hamiltonian
Boundary Value Problems Under Discretisation}, volume={20}, DOI={10.1007/s10208-020-09454-z},
number={6}, journal={Foundations of Computational Mathematics}, author={McLachlan,
Robert I and Offen, Christian}, year={2020}, pages={1363–1400} }'
chicago: 'McLachlan, Robert I, and Christian Offen. “Preservation of Bifurcations
of Hamiltonian Boundary Value Problems Under Discretisation.” Foundations of
Computational Mathematics 20, no. 6 (2020): 1363–1400. https://doi.org/10.1007/s10208-020-09454-z.'
ieee: R. I. McLachlan and C. Offen, “Preservation of Bifurcations of Hamiltonian
Boundary Value Problems Under Discretisation,” Foundations of Computational
Mathematics, vol. 20, no. 6, pp. 1363–1400, 2020.
mla: McLachlan, Robert I., and Christian Offen. “Preservation of Bifurcations of
Hamiltonian Boundary Value Problems Under Discretisation.” Foundations of Computational
Mathematics, vol. 20, no. 6, 2020, pp. 1363–400, doi:10.1007/s10208-020-09454-z.
short: R.I. McLachlan, C. Offen, Foundations of Computational Mathematics 20 (2020)
1363–1400.
date_created: 2020-10-06T16:31:46Z
date_updated: 2022-01-06T06:54:14Z
department:
- _id: '636'
doi: 10.1007/s10208-020-09454-z
extern: '1'
intvolume: ' 20'
issue: '6'
language:
- iso: eng
main_file_link:
- url: https://rdcu.be/b79aB
page: 1363-1400
publication: Foundations of Computational Mathematics
publication_status: published
status: public
title: Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation
type: journal_article
user_id: '85279'
volume: 20
year: '2020'
...
---
_id: '19939'
article_type: original
author:
- first_name: Lisa Maria
full_name: Kreusser, Lisa Maria
last_name: Kreusser
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
citation:
ama: Kreusser LM, McLachlan RI, Offen C. Detection of high codimensional bifurcations
in variational PDEs. Nonlinearity. 2020;33(5):2335-2363. doi:10.1088/1361-6544/ab7293
apa: Kreusser, L. M., McLachlan, R. I., & Offen, C. (2020). Detection of high
codimensional bifurcations in variational PDEs. Nonlinearity, 33(5),
2335–2363. https://doi.org/10.1088/1361-6544/ab7293
bibtex: '@article{Kreusser_McLachlan_Offen_2020, title={Detection of high codimensional
bifurcations in variational PDEs}, volume={33}, DOI={10.1088/1361-6544/ab7293},
number={5}, journal={Nonlinearity}, author={Kreusser, Lisa Maria and McLachlan,
Robert I and Offen, Christian}, year={2020}, pages={2335–2363} }'
chicago: 'Kreusser, Lisa Maria, Robert I McLachlan, and Christian Offen. “Detection
of High Codimensional Bifurcations in Variational PDEs.” Nonlinearity 33,
no. 5 (2020): 2335–63. https://doi.org/10.1088/1361-6544/ab7293.'
ieee: L. M. Kreusser, R. I. McLachlan, and C. Offen, “Detection of high codimensional
bifurcations in variational PDEs,” Nonlinearity, vol. 33, no. 5, pp. 2335–2363,
2020.
mla: Kreusser, Lisa Maria, et al. “Detection of High Codimensional Bifurcations
in Variational PDEs.” Nonlinearity, vol. 33, no. 5, 2020, pp. 2335–63,
doi:10.1088/1361-6544/ab7293.
short: L.M. Kreusser, R.I. McLachlan, C. Offen, Nonlinearity 33 (2020) 2335–2363.
date_created: 2020-10-06T16:32:04Z
date_updated: 2022-01-06T06:54:14Z
department:
- _id: '636'
doi: 10.1088/1361-6544/ab7293
extern: '1'
intvolume: ' 33'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1088/1361-6544/ab7293
oa: '1'
page: 2335-2363
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: Detection of high codimensional bifurcations in variational PDEs
type: journal_article
user_id: '85279'
volume: 33
year: '2020'
...
---
_id: '29399'
author:
- first_name: D. J. N.
full_name: Limebeer, D. J. N.
last_name: Limebeer
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: F. H.
full_name: Farshi, F. H.
last_name: Farshi
citation:
ama: Limebeer DJN, Ober-Blöbaum S, Farshi FH. Variational integrators for dissipative
systems. IEEE Transactions on Automatic Control. 2020;65(4):1381-1396.
apa: Limebeer, D. J. N., Ober-Blöbaum, S., & Farshi, F. H. (2020). Variational
integrators for dissipative systems. IEEE Transactions on Automatic Control,
65(4), 1381–1396.
bibtex: '@article{Limebeer_Ober-Blöbaum_Farshi_2020, title={Variational integrators
for dissipative systems}, volume={65(4)}, journal={IEEE Transactions on Automatic
Control}, author={Limebeer, D. J. N. and Ober-Blöbaum, Sina and Farshi, F. H.},
year={2020}, pages={1381–1396} }'
chicago: 'Limebeer, D. J. N., Sina Ober-Blöbaum, and F. H. Farshi. “Variational
Integrators for Dissipative Systems.” IEEE Transactions on Automatic Control
65(4) (2020): 1381–96.'
ieee: D. J. N. Limebeer, S. Ober-Blöbaum, and F. H. Farshi, “Variational integrators
for dissipative systems,” IEEE Transactions on Automatic Control, vol.
65(4), pp. 1381–1396, 2020.
mla: Limebeer, D. J. N., et al. “Variational Integrators for Dissipative Systems.”
IEEE Transactions on Automatic Control, vol. 65(4), 2020, pp. 1381–96.
short: D.J.N. Limebeer, S. Ober-Blöbaum, F.H. Farshi, IEEE Transactions on Automatic
Control 65(4) (2020) 1381–1396.
date_created: 2022-01-18T11:17:25Z
date_updated: 2022-01-21T08:26:46Z
department:
- _id: '636'
language:
- iso: eng
page: 1381-1396
publication: IEEE Transactions on Automatic Control
status: public
title: Variational integrators for dissipative systems
type: journal_article
user_id: '15694'
volume: 65(4)
year: '2020'
...
---
_id: '29398'
author:
- first_name: C. I. O.
full_name: Hernández Castellanos, C. I. O.
last_name: Hernández Castellanos
- first_name: G.
full_name: Schütze, G.
last_name: Schütze
- first_name: J.-Q.
full_name: Sun, J.-Q.
last_name: Sun
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: G.
full_name: Morales-Luna, G.
last_name: Morales-Luna
citation:
ama: Hernández Castellanos CIO, Schütze G, Sun J-Q, Ober-Blöbaum S, Morales-Luna
G. Numerical computation of lightly multi-objective robust optimal solutions by
means of generalized cell mapping. Mathematics. 2020;8(11):1959.
apa: Hernández Castellanos, C. I. O., Schütze, G., Sun, J.-Q., Ober-Blöbaum, S.,
& Morales-Luna, G. (2020). Numerical computation of lightly multi-objective
robust optimal solutions by means of generalized cell mapping. Mathematics,
8(11):1959.
bibtex: '@article{Hernández Castellanos_Schütze_Sun_Ober-Blöbaum_Morales-Luna_2020,
title={Numerical computation of lightly multi-objective robust optimal solutions
by means of generalized cell mapping}, volume={8(11):1959}, journal={Mathematics},
author={Hernández Castellanos, C. I. O. and Schütze, G. and Sun, J.-Q. and Ober-Blöbaum,
Sina and Morales-Luna, G.}, year={2020} }'
chicago: Hernández Castellanos, C. I. O., G. Schütze, J.-Q. Sun, Sina Ober-Blöbaum,
and G. Morales-Luna. “Numerical Computation of Lightly Multi-Objective Robust
Optimal Solutions by Means of Generalized Cell Mapping.” Mathematics 8(11):1959
(2020).
ieee: C. I. O. Hernández Castellanos, G. Schütze, J.-Q. Sun, S. Ober-Blöbaum, and
G. Morales-Luna, “Numerical computation of lightly multi-objective robust optimal
solutions by means of generalized cell mapping,” Mathematics, vol. 8(11):1959,
2020.
mla: Hernández Castellanos, C. I. O., et al. “Numerical Computation of Lightly Multi-Objective
Robust Optimal Solutions by Means of Generalized Cell Mapping.” Mathematics,
vol. 8(11):1959, 2020.
short: C.I.O. Hernández Castellanos, G. Schütze, J.-Q. Sun, S. Ober-Blöbaum, G.
Morales-Luna, Mathematics 8(11):1959 (2020).
date_created: 2022-01-18T11:08:28Z
date_updated: 2022-01-21T09:57:35Z
department:
- _id: '636'
language:
- iso: eng
publication: Mathematics
status: public
title: Numerical computation of lightly multi-objective robust optimal solutions by
means of generalized cell mapping
type: journal_article
user_id: '15694'
volume: 8(11):1959
year: '2020'
...
---
_id: '29422'
author:
- first_name: Y.
full_name: Lishkova, Y.
last_name: Lishkova
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: M.
full_name: Cannon, M.
last_name: Cannon
- first_name: S.
full_name: Leyendecker, S.
last_name: Leyendecker
citation:
ama: 'Lishkova Y, Ober-Blöbaum S, Cannon M, Leyendecker S. A multirate variational
approach to simulation and optimal control for flexible spacecraft. In: Accepted
for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference
- Lake Tahoe. ; 2020.'
apa: Lishkova, Y., Ober-Blöbaum, S., Cannon, M., & Leyendecker, S. (2020). A
multirate variational approach to simulation and optimal control for flexible
spacecraft. Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics
Specialist Conference - Lake Tahoe.
bibtex: '@inproceedings{Lishkova_Ober-Blöbaum_Cannon_Leyendecker_2020, title={A
multirate variational approach to simulation and optimal control for flexible
spacecraft}, booktitle={Accepted for publication in Proceedings of 2020 AAS/AIAA
Astrodynamics Specialist Conference - Lake Tahoe}, author={Lishkova, Y. and Ober-Blöbaum,
Sina and Cannon, M. and Leyendecker, S.}, year={2020} }'
chicago: Lishkova, Y., Sina Ober-Blöbaum, M. Cannon, and S. Leyendecker. “A Multirate
Variational Approach to Simulation and Optimal Control for Flexible Spacecraft.”
In Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist
Conference - Lake Tahoe, 2020.
ieee: Y. Lishkova, S. Ober-Blöbaum, M. Cannon, and S. Leyendecker, “A multirate
variational approach to simulation and optimal control for flexible spacecraft,”
2020.
mla: Lishkova, Y., et al. “A Multirate Variational Approach to Simulation and Optimal
Control for Flexible Spacecraft.” Accepted for Publication in Proceedings of
2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe, 2020.
short: 'Y. Lishkova, S. Ober-Blöbaum, M. Cannon, S. Leyendecker, in: Accepted for
Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference
- Lake Tahoe, 2020.'
date_created: 2022-01-18T14:37:53Z
date_updated: 2022-01-21T13:45:40Z
department:
- _id: '636'
language:
- iso: eng
publication: Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics
Specialist Conference - Lake Tahoe
status: public
title: A multirate variational approach to simulation and optimal control for flexible
spacecraft
type: conference
user_id: '15694'
year: '2020'
...
---
_id: '29423'
author:
- first_name: T.
full_name: Faulwasser, T.
last_name: Faulwasser
- first_name: K.
full_name: Flaßkamp, K.
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: 'K. '
full_name: 'Worthmann, K. '
last_name: Worthmann
citation:
ama: 'Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Worthmann K. A dissipativity characterization
of velocity turnpikes in optimal control problems for mechanical systems. In:
24th International Symposium on Mathematical Theory of Networks and Systems.
; 2020.'
apa: Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., & Worthmann, K. (2020).
A dissipativity characterization of velocity turnpikes in optimal control problems
for mechanical systems. 24th International Symposium on Mathematical Theory
of Networks and Systems.
bibtex: '@inproceedings{Faulwasser_Flaßkamp_Ober-Blöbaum_Worthmann_2020, title={A
dissipativity characterization of velocity turnpikes in optimal control problems
for mechanical systems}, booktitle={24th International Symposium on Mathematical
Theory of Networks and Systems}, author={Faulwasser, T. and Flaßkamp, K. and Ober-Blöbaum,
Sina and Worthmann, K. }, year={2020} }'
chicago: Faulwasser, T., K. Flaßkamp, Sina Ober-Blöbaum, and K. Worthmann. “A Dissipativity
Characterization of Velocity Turnpikes in Optimal Control Problems for Mechanical
Systems.” In 24th International Symposium on Mathematical Theory of Networks
and Systems, 2020.
ieee: T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, and K. Worthmann, “A dissipativity
characterization of velocity turnpikes in optimal control problems for mechanical
systems,” 2020.
mla: Faulwasser, T., et al. “A Dissipativity Characterization of Velocity Turnpikes
in Optimal Control Problems for Mechanical Systems.” 24th International Symposium
on Mathematical Theory of Networks and Systems, 2020.
short: 'T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, in: 24th International
Symposium on Mathematical Theory of Networks and Systems, 2020.'
date_created: 2022-01-18T14:42:07Z
date_updated: 2022-01-21T13:46:57Z
department:
- _id: '636'
language:
- iso: eng
publication: 24th International Symposium on Mathematical Theory of Networks and Systems
status: public
title: A dissipativity characterization of velocity turnpikes in optimal control problems
for mechanical systems
type: conference
user_id: '15694'
year: '2020'
...
---
_id: '29424'
author:
- first_name: 'J. '
full_name: 'Cresson, J. '
last_name: Cresson
- first_name: F.
full_name: Jiménez, F.
last_name: Jiménez
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Cresson J, Jiménez F, Ober-Blöbaum S. Modelling of the convection-diffusion
equation through fractional restricted calculus of variations. In: 24th International
Symposium on Mathematical Theory of Networks and Systems. ; 2020.'
apa: Cresson, J., Jiménez, F., & Ober-Blöbaum, S. (2020). Modelling of the convection-diffusion
equation through fractional restricted calculus of variations. 24th International
Symposium on Mathematical Theory of Networks and Systems.
bibtex: '@inproceedings{Cresson_Jiménez_Ober-Blöbaum_2020, title={Modelling of the
convection-diffusion equation through fractional restricted calculus of variations},
booktitle={24th International Symposium on Mathematical Theory of Networks and
Systems}, author={Cresson, J. and Jiménez, F. and Ober-Blöbaum, Sina}, year={2020}
}'
chicago: Cresson, J. , F. Jiménez, and Sina Ober-Blöbaum. “Modelling of the Convection-Diffusion
Equation through Fractional Restricted Calculus of Variations.” In 24th International
Symposium on Mathematical Theory of Networks and Systems, 2020.
ieee: J. Cresson, F. Jiménez, and S. Ober-Blöbaum, “Modelling of the convection-diffusion
equation through fractional restricted calculus of variations,” 2020.
mla: Cresson, J., et al. “Modelling of the Convection-Diffusion Equation through
Fractional Restricted Calculus of Variations.” 24th International Symposium
on Mathematical Theory of Networks and Systems, 2020.
short: 'J. Cresson, F. Jiménez, S. Ober-Blöbaum, in: 24th International Symposium
on Mathematical Theory of Networks and Systems, 2020.'
date_created: 2022-01-18T14:45:22Z
date_updated: 2022-01-21T13:47:49Z
department:
- _id: '636'
language:
- iso: eng
publication: 24th International Symposium on Mathematical Theory of Networks and Systems
status: public
title: Modelling of the convection-diffusion equation through fractional restricted
calculus of variations
type: conference
user_id: '15694'
year: '2020'
...
---
_id: '29545'
author:
- first_name: Frédéric
full_name: Jean, Frédéric
last_name: Jean
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Igor
full_name: Zelenko, Igor
last_name: Zelenko
citation:
ama: Jean F, Maslovskaya S, Zelenko I. On Weyl’s type theorems and genericity of
projective rigidity in sub-Riemannian geometry. Geometriae Dedicata. 2020;213(1):295-314.
doi:10.1007/s10711-020-00581-z
apa: Jean, F., Maslovskaya, S., & Zelenko, I. (2020). On Weyl’s type theorems
and genericity of projective rigidity in sub-Riemannian geometry. Geometriae
Dedicata, 213(1), 295–314. https://doi.org/10.1007/s10711-020-00581-z
bibtex: '@article{Jean_Maslovskaya_Zelenko_2020, title={On Weyl’s type theorems
and genericity of projective rigidity in sub-Riemannian geometry}, volume={213},
DOI={10.1007/s10711-020-00581-z},
number={1}, journal={Geometriae Dedicata}, publisher={Springer Science and Business
Media LLC}, author={Jean, Frédéric and Maslovskaya, Sofya and Zelenko, Igor},
year={2020}, pages={295–314} }'
chicago: 'Jean, Frédéric, Sofya Maslovskaya, and Igor Zelenko. “On Weyl’s Type Theorems
and Genericity of Projective Rigidity in Sub-Riemannian Geometry.” Geometriae
Dedicata 213, no. 1 (2020): 295–314. https://doi.org/10.1007/s10711-020-00581-z.'
ieee: 'F. Jean, S. Maslovskaya, and I. Zelenko, “On Weyl’s type theorems and genericity
of projective rigidity in sub-Riemannian geometry,” Geometriae Dedicata,
vol. 213, no. 1, pp. 295–314, 2020, doi: 10.1007/s10711-020-00581-z.'
mla: Jean, Frédéric, et al. “On Weyl’s Type Theorems and Genericity of Projective
Rigidity in Sub-Riemannian Geometry.” Geometriae Dedicata, vol. 213, no.
1, Springer Science and Business Media LLC, 2020, pp. 295–314, doi:10.1007/s10711-020-00581-z.
short: F. Jean, S. Maslovskaya, I. Zelenko, Geometriae Dedicata 213 (2020) 295–314.
date_created: 2022-01-26T13:19:18Z
date_updated: 2022-01-26T13:19:39Z
department:
- _id: '636'
doi: 10.1007/s10711-020-00581-z
intvolume: ' 213'
issue: '1'
keyword:
- Geometry and Topology
language:
- iso: eng
page: 295-314
publication: Geometriae Dedicata
publication_identifier:
issn:
- 0046-5755
- 1572-9168
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian
geometry
type: journal_article
user_id: '87909'
volume: 213
year: '2020'
...
---
_id: '29546'
author:
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Jean-Baptiste
full_name: Caillau, Jean-Baptiste
last_name: Caillau
- first_name: Walid
full_name: Djema, Walid
last_name: Djema
- first_name: Laetitia
full_name: Giraldi, Laetitia
last_name: Giraldi
- first_name: Jean-Luc
full_name: Jean-Luc, Jean-Luc
last_name: Jean-Luc
- first_name: Jean-Baptiste
full_name: Pomet, Jean-Baptiste
last_name: Pomet
citation:
ama: 'Maslovskaya S, Caillau J-B, Djema W, Giraldi L, Jean-Luc J-L, Pomet J-B. The
turnpike property in maximization of microbial metabolite production. In: ; 2020.'
apa: Maslovskaya, S., Caillau, J.-B., Djema, W., Giraldi, L., Jean-Luc, J.-L., &
Pomet, J.-B. (2020). The turnpike property in maximization of microbial metabolite
production. IFAC 2020 - 21rst IFAC World Congress.
bibtex: '@inproceedings{Maslovskaya_Caillau_Djema_Giraldi_Jean-Luc_Pomet_2020, title={The
turnpike property in maximization of microbial metabolite production}, author={Maslovskaya,
Sofya and Caillau, Jean-Baptiste and Djema, Walid and Giraldi, Laetitia and Jean-Luc,
Jean-Luc and Pomet, Jean-Baptiste}, year={2020} }'
chicago: Maslovskaya, Sofya, Jean-Baptiste Caillau, Walid Djema, Laetitia Giraldi,
Jean-Luc Jean-Luc, and Jean-Baptiste Pomet. “The Turnpike Property in Maximization
of Microbial Metabolite Production,” 2020.
ieee: S. Maslovskaya, J.-B. Caillau, W. Djema, L. Giraldi, J.-L. Jean-Luc, and J.-B.
Pomet, “The turnpike property in maximization of microbial metabolite production,”
presented at the IFAC 2020 - 21rst IFAC World Congress, 2020.
mla: Maslovskaya, Sofya, et al. The Turnpike Property in Maximization of Microbial
Metabolite Production. 2020.
short: 'S. Maslovskaya, J.-B. Caillau, W. Djema, L. Giraldi, J.-L. Jean-Luc, J.-B.
Pomet, in: 2020.'
conference:
name: IFAC 2020 - 21rst IFAC World Congress
date_created: 2022-01-26T13:26:36Z
date_updated: 2022-01-26T13:39:01Z
department:
- _id: '636'
extern: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://hal.archives-ouvertes.fr/hal-02916081/document
oa: '1'
quality_controlled: '1'
status: public
title: The turnpike property in maximization of microbial metabolite production
type: conference_abstract
user_id: '87909'
year: '2020'
...
---
_id: '29413'
author:
- first_name: K.
full_name: Flaßkamp, K.
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: 'S. '
full_name: 'Peitz, S. '
last_name: Peitz
citation:
ama: 'Flaßkamp K, Ober-Blöbaum S, Peitz S. Symmetry in optimal control: A multiobjective
model predictive control approach. In: Junge O, Schütze O, Froyland G, Ober-Blöbaum
S, Padberg-Gehle K, eds. Advances in Dynamics, Optimization and Computation.
Springer International Publishing; 2020:209-237.'
apa: 'Flaßkamp, K., Ober-Blöbaum, S., & Peitz, S. (2020). Symmetry in optimal
control: A multiobjective model predictive control approach. In O. Junge, O. Schütze,
G. Froyland, S. Ober-Blöbaum, & K. Padberg-Gehle (Eds.), Advances in Dynamics,
Optimization and Computation (pp. 209–237). Springer International Publishing.'
bibtex: '@inbook{Flaßkamp_Ober-Blöbaum_Peitz_2020, place={Cham}, title={Symmetry
in optimal control: A multiobjective model predictive control approach}, booktitle={Advances
in Dynamics, Optimization and Computation}, publisher={Springer International
Publishing}, author={Flaßkamp, K. and Ober-Blöbaum, Sina and Peitz, S. }, editor={Junge,
Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle,
Kathrin}, year={2020}, pages={209–237} }'
chicago: 'Flaßkamp, K., Sina Ober-Blöbaum, and S. Peitz. “Symmetry in Optimal Control:
A Multiobjective Model Predictive Control Approach.” In Advances in Dynamics,
Optimization and Computation, edited by Oliver Junge, Oliver Schütze, Gary
Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle, 209–37. Cham: Springer
International Publishing, 2020.'
ieee: 'K. Flaßkamp, S. Ober-Blöbaum, and S. Peitz, “Symmetry in optimal control:
A multiobjective model predictive control approach,” in Advances in Dynamics,
Optimization and Computation, O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum,
and K. Padberg-Gehle, Eds. Cham: Springer International Publishing, 2020, pp.
209–237.'
mla: 'Flaßkamp, K., et al. “Symmetry in Optimal Control: A Multiobjective Model
Predictive Control Approach.” Advances in Dynamics, Optimization and Computation,
edited by Oliver Junge et al., Springer International Publishing, 2020, pp. 209–37.'
short: 'K. Flaßkamp, S. Ober-Blöbaum, S. Peitz, in: O. Junge, O. Schütze, G. Froyland,
S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and
Computation, Springer International Publishing, Cham, 2020, pp. 209–237.'
date_created: 2022-01-18T12:58:18Z
date_updated: 2023-11-08T08:15:14Z
department:
- _id: '636'
editor:
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Kathrin
full_name: Padberg-Gehle, Kathrin
last_name: Padberg-Gehle
language:
- iso: eng
page: 209-237
place: Cham
publication: Advances in Dynamics, Optimization and Computation
publisher: Springer International Publishing
status: public
title: 'Symmetry in optimal control: A multiobjective model predictive control approach'
type: book_chapter
user_id: '15694'
year: '2020'
...
---
_id: '19945'
abstract:
- lang: eng
text: Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations,
…) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian
systems on manifolds equipped with Poisson brackets. The Poisson structure is
connected to conservation properties and other geometric features of solutions
to the PDE and, therefore, of great interest for numerical integration. For the
example of Burgers' equations and related PDEs we use Clebsch variables to lift
the original system to a collective Hamiltonian system on a symplectic manifold
whose structure is related to the original Lie-Poisson structure. On the collective
Hamiltonian system a symplectic integrator can be applied. Our numerical examples
show excellent conservation properties and indicate that the disadvantage of an
increased phase-space dimension can be outweighed by the advantage of symplectic
integration.
article_type: original
author:
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
- first_name: Benjamin K
full_name: Tapley, Benjamin K
last_name: Tapley
citation:
ama: McLachlan RI, Offen C, Tapley BK. Symplectic integration of PDEs using Clebsch
variables. Journal of Computational Dynamics. 2019;6(1):111-130. doi:10.3934/jcd.2019005
apa: McLachlan, R. I., Offen, C., & Tapley, B. K. (2019). Symplectic integration
of PDEs using Clebsch variables. Journal of Computational Dynamics, 6(1),
111–130. https://doi.org/10.3934/jcd.2019005
bibtex: '@article{McLachlan_Offen_Tapley_2019, title={Symplectic integration of
PDEs using Clebsch variables}, volume={6}, DOI={10.3934/jcd.2019005},
number={1}, journal={Journal of Computational Dynamics}, publisher={American Institute
of Mathematical Sciences (AIMS)}, author={McLachlan, Robert I and Offen, Christian
and Tapley, Benjamin K}, year={2019}, pages={111–130} }'
chicago: 'McLachlan, Robert I, Christian Offen, and Benjamin K Tapley. “Symplectic
Integration of PDEs Using Clebsch Variables.” Journal of Computational Dynamics
6, no. 1 (2019): 111–30. https://doi.org/10.3934/jcd.2019005.'
ieee: R. I. McLachlan, C. Offen, and B. K. Tapley, “Symplectic integration of PDEs
using Clebsch variables,” Journal of Computational Dynamics, vol. 6, no.
1, pp. 111–130, 2019.
mla: McLachlan, Robert I., et al. “Symplectic Integration of PDEs Using Clebsch
Variables.” Journal of Computational Dynamics, vol. 6, no. 1, American
Institute of Mathematical Sciences (AIMS), 2019, pp. 111–30, doi:10.3934/jcd.2019005.
short: R.I. McLachlan, C. Offen, B.K. Tapley, Journal of Computational Dynamics
6 (2019) 111–130.
date_created: 2020-10-06T16:44:07Z
date_updated: 2022-01-06T06:54:15Z
department:
- _id: '636'
doi: 10.3934/jcd.2019005
extern: '1'
intvolume: ' 6'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.aimsciences.org/article/doi/10.3934/jcd.2019005
oa: '1'
page: 111-130
publication: Journal of Computational Dynamics
publication_identifier:
issn:
- 2158-2505
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: Symplectic integration of PDEs using Clebsch variables
type: journal_article
user_id: '85279'
volume: 6
year: '2019'
...
---
_id: '29867'
author:
- first_name: Tim
full_name: Faulwasser, Tim
last_name: Faulwasser
- first_name: K.
full_name: Flaßkamp, K.
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: 'Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Worthmann K. Towards velocity turnpikes
in optimal control of mechanical systems. In: IFAC-PapersOnLine, ed. Vol 52(16).
; 2019:490-495.'
apa: 'Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., & Worthmann, K. (2019).
Towards velocity turnpikes in optimal control of mechanical systems: Vol. 52(16)
(IFAC-PapersOnLine, Ed.; pp. 490–495).'
bibtex: '@inproceedings{Faulwasser_Flaßkamp_Ober-Blöbaum_Worthmann_2019, title={Towards
velocity turnpikes in optimal control of mechanical systems}, volume={52(16)},
author={Faulwasser, Tim and Flaßkamp, K. and Ober-Blöbaum, Sina and Worthmann,
Karl}, editor={IFAC-PapersOnLine}, year={2019}, pages={490–495} }'
chicago: Faulwasser, Tim, K. Flaßkamp, Sina Ober-Blöbaum, and Karl Worthmann. “Towards
Velocity Turnpikes in Optimal Control of Mechanical Systems.” edited by IFAC-PapersOnLine,
52(16):490–95, 2019.
ieee: T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, and K. Worthmann, “Towards velocity
turnpikes in optimal control of mechanical systems,” 2019, vol. 52(16), pp. 490–495.
mla: Faulwasser, Tim, et al. Towards Velocity Turnpikes in Optimal Control of
Mechanical Systems. Edited by IFAC-PapersOnLine, vol. 52(16), 2019, pp. 490–95.
short: 'T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, in: IFAC-PapersOnLine
(Ed.), 2019, pp. 490–495.'
corporate_editor:
- IFAC-PapersOnLine
date_created: 2022-02-17T07:23:52Z
date_updated: 2023-11-08T08:09:01Z
department:
- _id: '636'
language:
- iso: eng
page: 490-495
status: public
title: Towards velocity turnpikes in optimal control of mechanical systems
type: conference
user_id: '15694'
volume: 52(16)
year: '2019'
...
---
_id: '19935'
abstract:
- lang: eng
text: 'A bifurcation is a qualitative change in a family of solutions to an equation
produced by varying parameters. In contrast to the local bifurcations of dynamical
systems that are often related to a change in the number or stability of equilibria,
bifurcations of boundary value problems are global in nature and may not be related
to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed
framework which studies the bifurcations of critical points of functions. In this
paper we study the bifurcations of solutions of boundary-value problems for symplectic
maps, using the language of (finite-dimensional) singularity theory. We associate
certain such problems with a geometric picture involving the intersection of Lagrangian
submanifolds, and hence with the critical points of a suitable generating function.
Within this framework, we then study the effect of three special cases: (i) some
common boundary conditions, such as Dirichlet boundary conditions for second-order
systems, restrict the possible types of bifurcations (for example, in generic
planar systems only the A-series beginning with folds and cusps can occur); (ii)
integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic
pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing
symmetries can exhibit restricted bifurcations associated with the symmetry. This
approach offers an alternative to the analysis of critical points in function
spaces, typically used in the study of bifurcation of variational problems, and
opens the way to the detection of more exotic bifurcations than the simple folds
and cusps that are often found in examples. '
article_type: original
author:
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
citation:
ama: McLachlan RI, Offen C. Bifurcation of solutions to Hamiltonian boundary value
problems. Nonlinearity. 2018:2895-2927. doi:10.1088/1361-6544/aab630
apa: McLachlan, R. I., & Offen, C. (2018). Bifurcation of solutions to Hamiltonian
boundary value problems. Nonlinearity, 2895–2927. https://doi.org/10.1088/1361-6544/aab630
bibtex: '@article{McLachlan_Offen_2018, title={Bifurcation of solutions to Hamiltonian
boundary value problems}, DOI={10.1088/1361-6544/aab630},
journal={Nonlinearity}, author={McLachlan, Robert I and Offen, Christian}, year={2018},
pages={2895–2927} }'
chicago: McLachlan, Robert I, and Christian Offen. “Bifurcation of Solutions to
Hamiltonian Boundary Value Problems.” Nonlinearity, 2018, 2895–2927. https://doi.org/10.1088/1361-6544/aab630.
ieee: R. I. McLachlan and C. Offen, “Bifurcation of solutions to Hamiltonian boundary
value problems,” Nonlinearity, pp. 2895–2927, 2018.
mla: McLachlan, Robert I., and Christian Offen. “Bifurcation of Solutions to Hamiltonian
Boundary Value Problems.” Nonlinearity, 2018, pp. 2895–927, doi:10.1088/1361-6544/aab630.
short: R.I. McLachlan, C. Offen, Nonlinearity (2018) 2895–2927.
date_created: 2020-10-06T16:28:36Z
date_updated: 2022-01-06T06:54:14Z
department:
- _id: '636'
doi: 10.1088/1361-6544/aab630
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://doi.org/10.1088/1361-6544/aab630
page: 2895-2927
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: Bifurcation of solutions to Hamiltonian boundary value problems
type: journal_article
user_id: '85279'
year: '2018'
...
---
_id: '19937'
abstract:
- lang: eng
text: Symplectic integrators can be excellent for Hamiltonian initial value problems.
Reasons for this include their preservation of invariant sets like tori, good
energy behaviour, nonexistence of attractors, and good behaviour of statistical
properties. These all refer to {\em long-time} behaviour. They are directly connected
to the dynamical behaviour of symplectic maps φ:M→M' on the phase space under
iteration. Boundary value problems, in contrast, are posed for fixed (and often
quite short) times. Symplecticity manifests as a symplectic map φ:M→M' which is
not iterated. Is there any point, therefore, for a symplectic integrator to be
used on a Hamiltonian boundary value problem? In this paper we announce results
that symplectic integrators preserve bifurcations of Hamiltonian boundary value
problems and that nonsymplectic integrators do not.
article_type: original
author:
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
citation:
ama: McLachlan RI, Offen C. Symplectic integration of boundary value problems. Numerical
Algorithms. 2018:1219-1233. doi:10.1007/s11075-018-0599-7
apa: McLachlan, R. I., & Offen, C. (2018). Symplectic integration of boundary
value problems. Numerical Algorithms, 1219–1233. https://doi.org/10.1007/s11075-018-0599-7
bibtex: '@article{McLachlan_Offen_2018, title={Symplectic integration of boundary
value problems}, DOI={10.1007/s11075-018-0599-7},
journal={Numerical Algorithms}, author={McLachlan, Robert I and Offen, Christian},
year={2018}, pages={1219–1233} }'
chicago: McLachlan, Robert I, and Christian Offen. “Symplectic Integration of Boundary
Value Problems.” Numerical Algorithms, 2018, 1219–33. https://doi.org/10.1007/s11075-018-0599-7.
ieee: R. I. McLachlan and C. Offen, “Symplectic integration of boundary value problems,”
Numerical Algorithms, pp. 1219–1233, 2018.
mla: McLachlan, Robert I., and Christian Offen. “Symplectic Integration of Boundary
Value Problems.” Numerical Algorithms, 2018, pp. 1219–33, doi:10.1007/s11075-018-0599-7.
short: R.I. McLachlan, C. Offen, Numerical Algorithms (2018) 1219–1233.
date_created: 2020-10-06T16:29:14Z
date_updated: 2022-01-06T06:54:14Z
department:
- _id: '636'
doi: 10.1007/s11075-018-0599-7
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://rdcu.be/b79ap
page: 1219-1233
publication: Numerical Algorithms
publication_identifier:
issn:
- 1017-1398
- 1572-9265
publication_status: published
status: public
title: Symplectic integration of boundary value problems
type: journal_article
user_id: '85279'
year: '2018'
...
---
_id: '29425'
author:
- first_name: F.
full_name: Jiménez, F.
last_name: Jiménez
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Jiménez F, Ober-Blöbaum S. Necessary optimality conditions for optimally controlled
dissipative mechanical systems modelled through fractional derivatives. In: 6th
European Conference on Computational Mechanics. ; 2018.'
apa: Jiménez, F., & Ober-Blöbaum, S. (2018). Necessary optimality conditions
for optimally controlled dissipative mechanical systems modelled through fractional
derivatives. 6th European Conference on Computational Mechanics.
bibtex: '@inproceedings{Jiménez_Ober-Blöbaum_2018, title={Necessary optimality conditions
for optimally controlled dissipative mechanical systems modelled through fractional
derivatives}, booktitle={6th European Conference on Computational Mechanics},
author={Jiménez, F. and Ober-Blöbaum, Sina}, year={2018} }'
chicago: Jiménez, F., and Sina Ober-Blöbaum. “Necessary Optimality Conditions for
Optimally Controlled Dissipative Mechanical Systems Modelled through Fractional
Derivatives.” In 6th European Conference on Computational Mechanics, 2018.
ieee: F. Jiménez and S. Ober-Blöbaum, “Necessary optimality conditions for optimally
controlled dissipative mechanical systems modelled through fractional derivatives,”
2018.
mla: Jiménez, F., and Sina Ober-Blöbaum. “Necessary Optimality Conditions for Optimally
Controlled Dissipative Mechanical Systems Modelled through Fractional Derivatives.”
6th European Conference on Computational Mechanics, 2018.
short: 'F. Jiménez, S. Ober-Blöbaum, in: 6th European Conference on Computational
Mechanics, 2018.'
conference:
end_date: 2018-06-15
start_date: 2018-06-11
date_created: 2022-01-18T14:49:40Z
date_updated: 2022-01-21T13:51:41Z
department:
- _id: '636'
language:
- iso: eng
publication: 6th European Conference on Computational Mechanics
status: public
title: Necessary optimality conditions for optimally controlled dissipative mechanical
systems modelled through fractional derivatives
type: conference
user_id: '15694'
year: '2018'
...
---
_id: '29427'
author:
- first_name: F.
full_name: Jiménez, F.
last_name: Jiménez
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Jiménez F, Ober-Blöbaum S. A fractional variational approach for modelling
dissipative mechanical systems continuous and discrete settings. In: IFAC-PapersOnLine,
ed. 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control
LHMNC 2018. Vol 51(3). ; 2018:50-55.'
apa: 'Jiménez, F., & Ober-Blöbaum, S. (2018). A fractional variational approach
for modelling dissipative mechanical systems continuous and discrete settings.
In IFAC-PapersOnLine (Ed.), 6th IFAC Workshop on Lagrangian and Hamiltonian
Methods for Nonlinear Control LHMNC 2018: Vol. 51(3) (pp. 50–55).'
bibtex: '@inproceedings{Jiménez_Ober-Blöbaum_2018, title={A fractional variational
approach for modelling dissipative mechanical systems continuous and discrete
settings}, volume={51(3)}, booktitle={6th IFAC Workshop on Lagrangian and Hamiltonian
Methods for Nonlinear Control LHMNC 2018}, author={Jiménez, F. and Ober-Blöbaum,
Sina}, editor={IFAC-PapersOnLine}, year={2018}, pages={50–55} }'
chicago: Jiménez, F., and Sina Ober-Blöbaum. “A Fractional Variational Approach
for Modelling Dissipative Mechanical Systems Continuous and Discrete Settings.”
In 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control
LHMNC 2018, edited by IFAC-PapersOnLine, 51(3):50–55, 2018.
ieee: F. Jiménez and S. Ober-Blöbaum, “A fractional variational approach for modelling
dissipative mechanical systems continuous and discrete settings,” in 6th IFAC
Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018,
2018, vol. 51(3), pp. 50–55.
mla: Jiménez, F., and Sina Ober-Blöbaum. “A Fractional Variational Approach for
Modelling Dissipative Mechanical Systems Continuous and Discrete Settings.” 6th
IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC
2018, edited by IFAC-PapersOnLine, vol. 51(3), 2018, pp. 50–55.
short: 'F. Jiménez, S. Ober-Blöbaum, in: IFAC-PapersOnLine (Ed.), 6th IFAC Workshop
on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018, 2018,
pp. 50–55.'
corporate_editor:
- IFAC-PapersOnLine
date_created: 2022-01-18T14:55:51Z
date_updated: 2022-01-21T13:53:24Z
department:
- _id: '636'
language:
- iso: eng
page: 50-55
publication: 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear
Control LHMNC 2018
status: public
title: A fractional variational approach for modelling dissipative mechanical systems
continuous and discrete settings
type: conference
user_id: '15694'
volume: 51(3)
year: '2018'
...
---
_id: '19940'
abstract:
- lang: eng
text: "Two smooth map germs are right-equivalent if and only if they generate two\r\nLagrangian
submanifolds in a cotangent bundle which have the same contact with\r\nthe zero-section.
In this paper we provide a reverse direction to this\r\nclassical result of Golubitsky
and Guillemin. Two Lagrangian submanifolds of a\r\nsymplectic manifold have the
same contact with a third Lagrangian submanifold\r\nif and only if the intersection
problems correspond to stably right equivalent\r\nmap germs. We, therefore, obtain
a correspondence between local Lagrangian\r\nintersection problems and catastrophe
theory while the classical version only\r\ncaptures tangential intersections.
The correspondence is defined independently\r\nof any Lagrangian fibration of
the ambient symplectic manifold, in contrast to\r\nother classical results. Moreover,
we provide an extension of the\r\ncorrespondence to families of local Lagrangian
intersection problems. This\r\ngives rise to a framework which allows a natural
transportation of the notions\r\nof catastrophe theory such as stability, unfolding
and (uni-)versality to the\r\ngeometric setting such that we obtain a classification
of families of local\r\nLagrangian intersection problems. An application is the
classification of\r\nLagrangian boundary value problems for symplectic maps."
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
citation:
ama: Offen C. Local intersections of Lagrangian manifolds correspond to catastrophe
theory. arXiv:181110165.
apa: Offen, C. (n.d.). Local intersections of Lagrangian manifolds correspond to
catastrophe theory. In arXiv:1811.10165.
bibtex: '@article{Offen, title={Local intersections of Lagrangian manifolds correspond
to catastrophe theory}, journal={arXiv:1811.10165}, author={Offen, Christian}
}'
chicago: Offen, Christian. “Local Intersections of Lagrangian Manifolds Correspond
to Catastrophe Theory.” ArXiv:1811.10165, n.d.
ieee: C. Offen, “Local intersections of Lagrangian manifolds correspond to catastrophe
theory,” arXiv:1811.10165. .
mla: Offen, Christian. “Local Intersections of Lagrangian Manifolds Correspond to
Catastrophe Theory.” ArXiv:1811.10165.
short: C. Offen, ArXiv:1811.10165 (n.d.).
date_created: 2020-10-06T16:32:45Z
date_updated: 2023-08-10T08:48:55Z
ddc:
- '510'
department:
- _id: '636'
external_id:
arxiv:
- '1811.10165'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2021-12-21T16:01:03Z
date_updated: 2021-12-21T16:01:03Z
description: |-
Two smooth map germs are right-equivalent if and only if they
generate two Lagrangian submanifolds in a cotangent bundle which have the
same contact with the zero-section. In this paper we provide a reverse direction
to this classical result of Golubitsky and Guillemin. Two Lagrangian submanifolds of a symplectic manifold have the same contact with a third Lagrangian
submanifold if and only if the intersection problems correspond to stably right
equivalent map germs. We, therefore, obtain a correspondence between local
Lagrangian intersection problems and catastrophe theory while the classical
version only captures tangential intersections. The correspondence is defined
independently of any Lagrangian fibration of the ambient symplectic manifold, in contrast to other classical results. Moreover, we provide an extension
of the correspondence to families of local Lagrangian intersection problems.
This gives rise to a framework which allows a natural transportation of the
notions of catastrophe theory such as stability, unfolding and (uni-)versality
to the geometric setting such that we obtain a classification of families of lo-
cal Lagrangian intersection problems. An application is the classification of
Lagrangian boundary value problems for symplectic maps.
file_id: '29078'
file_name: LocalLagrangianContact.pdf
file_size: 662483
relation: main_file
title: Local intersections of Lagrangian manifolds correspond to catastrophe theory
file_date_updated: 2021-12-21T16:01:03Z
has_accepted_license: '1'
language:
- iso: eng
oa: '1'
publication: arXiv:1811.10165
publication_status: submitted
status: public
title: Local intersections of Lagrangian manifolds correspond to catastrophe theory
type: preprint
user_id: '85279'
year: '2018'
...
---
_id: '19943'
abstract:
- lang: eng
text: 'In this paper we continue our study of bifurcations of solutions of boundary-value
problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have
been shown to be connected to catastrophe theory via generating functions and
ordinary and reversal phase space symmetries have been considered. Here we present
a convenient, coordinate free framework to analyse separated Lagrangian boundary
value problems which include classical Dirichlet, Neumann and Robin boundary value
problems. The framework is then used to prove the existence of obstructions arising
from conformal symplectic symmetries on the bifurcation behaviour of solutions
to Hamiltonian boundary value problems. Under non-degeneracy conditions, a group
action by conformal symplectic symmetries has the effect that the flow map cannot
degenerate in a direction which is tangential to the action. This imposes restrictions
on which singularities can occur in boundary value problems. Our results generalise
classical results about conjugate loci on Riemannian manifolds to a large class
of Hamiltonian boundary value problems with, for example, scaling symmetries. '
article_type: original
author:
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
citation:
ama: McLachlan RI, Offen C. Hamiltonian boundary value problems, conformal symplectic
symmetries, and conjugate loci. New Zealand Journal of Mathematics. 2018;48:83-99.
doi:10.53733/34
apa: McLachlan, R. I., & Offen, C. (2018). Hamiltonian boundary value problems,
conformal symplectic symmetries, and conjugate loci. New Zealand Journal of
Mathematics, 48, 83–99. https://doi.org/10.53733/34
bibtex: '@article{McLachlan_Offen_2018, title={Hamiltonian boundary value problems,
conformal symplectic symmetries, and conjugate loci}, volume={48}, DOI={10.53733/34 }, journal={New Zealand Journal of Mathematics}, author={McLachlan,
Robert I and Offen, Christian}, year={2018}, pages={83–99} }'
chicago: 'McLachlan, Robert I, and Christian Offen. “Hamiltonian Boundary Value
Problems, Conformal Symplectic Symmetries, and Conjugate Loci.” New Zealand
Journal of Mathematics 48 (2018): 83–99. https://doi.org/10.53733/34 .'
ieee: 'R. I. McLachlan and C. Offen, “Hamiltonian boundary value problems, conformal
symplectic symmetries, and conjugate loci,” New Zealand Journal of Mathematics,
vol. 48, pp. 83–99, 2018, doi: 10.53733/34
.'
mla: McLachlan, Robert I., and Christian Offen. “Hamiltonian Boundary Value Problems,
Conformal Symplectic Symmetries, and Conjugate Loci.” New Zealand Journal of
Mathematics, vol. 48, 2018, pp. 83–99, doi:10.53733/34 .
short: R.I. McLachlan, C. Offen, New Zealand Journal of Mathematics 48 (2018) 83–99.
date_created: 2020-10-06T16:39:08Z
date_updated: 2023-09-21T07:29:24Z
ddc:
- '510'
department:
- _id: '636'
doi: '10.53733/34 '
extern: '1'
external_id:
arxiv:
- '1804.07479'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2020-10-06T16:49:29Z
date_updated: 2020-10-07T14:04:01Z
file_id: '19946'
file_name: Hamiltonian_Boundary_Value_Problems,_Conformal_Symplectic_Symmetries,_and_Conjugate_Loci.pdf
file_size: 3126111
relation: main_file
title: Hamiltonian Boundary Value Problems, Conformal Symplectic Symmetries, and
Conjugate Loci
file_date_updated: 2020-10-07T14:04:01Z
has_accepted_license: '1'
intvolume: ' 48'
keyword:
- Hamiltonian boundary value problems
- singularities
- conformal symplectic geometry
- catastrophe theory
- conjugate loci
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://nzjmath.org/index.php/NZJMATH/article/view/34
oa: '1'
page: 83-99
publication: New Zealand Journal of Mathematics
publication_status: published
quality_controlled: '1'
status: public
title: Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate
loci
type: journal_article
user_id: '85279'
volume: 48
year: '2018'
...