---
_id: '63253'
abstract:
- lang: eng
text: "Abstract\r\n The Neumann problem
for the Keller-Segel system \r\n \r\n
\ \r\n \r\n \r\n \r\n
\ \r\n \r\n
\ {\r\n \r\n \r\n
\ \r\n \r\n
\ u\r\n t\r\n
\ \r\n =\r\n
\ ∇\r\n
\ ⋅\r\n \r\n
\ (\r\n D\r\n
\ \r\n (\r\n
\ u\r\n )\r\n
\ \r\n ∇\r\n u\r\n
\ )\r\n \r\n
\ −\r\n ∇\r\n ⋅\r\n
\ \r\n (\r\n
\ S\r\n \r\n
\ (\r\n u\r\n
\ )\r\n \r\n
\ ∇\r\n
\ v\r\n )\r\n
\ \r\n ,\r\n
\ \r\n \r\n
\ \r\n \r\n
\ 0\r\n =\r\n
\ Δ\r\n
\ v\r\n −\r\n
\ μ\r\n +\r\n
\ u\r\n ,\r\n
\ \r\n
\ μ\r\n =\r\n
\ \r\n −\r\n
\ \r\n
\ \r\n
\ \r\n
\ \r\n
\ \r\n
\ \r\n
\ \r\n
\ \r\n
\ \r\n
\ \r\n ∫\r\n
\ Ω\r\n
\ \r\n u\r\n
\ d\r\n
\ x\r\n ,\r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
is considered in n-dimensional balls Ω with \r\n
\ \r\n \r\n \r\n n\r\n
\ ⩾\r\n 2\r\n
\ \r\n \r\n ,
with suitably regular and radially symmetric, radially nonincreasing initial data
u\r\n 0. The
functions D and S are only
assumed to belong to \r\n \r\n
\ \r\n \r\n \r\n
\ C\r\n 2\r\n
\ \r\n (\r\n
\ [\r\n 0\r\n
\ ,\r\n ∞\r\n )\r\n
\ )\r\n \r\n
\ \r\n and
to satisfy D > 0 and \r\n \r\n
\ \r\n \r\n S\r\n
\ ⩾\r\n 0\r\n
\ \r\n \r\n
on \r\n \r\n \r\n \r\n
\ [\r\n 0\r\n
\ ,\r\n ∞\r\n )\r\n
\ \r\n \r\n
as well as \r\n \r\n
\ \r\n \r\n S\r\n
\ (\r\n 0\r\n
\ )\r\n =\r\n
\ 0\r\n \r\n
\ \r\n ;
in particular, diffusivities with arbitrarily fast decay are included.\r\n
\ In this general context, it is shown that it is merely
the asymptotic behavior as \r\n \r\n
\ \r\n \r\n ξ\r\n
\ →\r\n
\ ∞\r\n \r\n
\ \r\n of
the expression \r\n \r\n
\ \r\n \r\n \r\n \r\n
\ \r\n I\r\n
\ \r\n (\r\n
\ ξ\r\n )\r\n
\ \r\n :=\r\n
\ \r\n \r\n
\ S\r\n \r\n
\ (\r\n ξ\r\n
\ )\r\n \r\n
\ \r\n \r\n
\ \r\n ξ\r\n
\ \r\n 2\r\n
\ n\r\n \r\n
\ \r\n D\r\n
\ \r\n (\r\n
\ ξ\r\n )\r\n
\ \r\n \r\n
\ \r\n ,\r\n
\ \r\n ξ\r\n
\ >\r\n 0\r\n
\ ,\r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
which decides about the occurrence of blow-up: Namely, it is seen that\r\n\r\n \r\n •\r\n
\ if \r\n \r\n
\ \r\n \r\n \r\n
\ lim\r\n
\ \r\n ξ\r\n
\ →\r\n
\ ∞\r\n
\ \r\n \r\n
\ I\r\n (\r\n ξ\r\n
\ )\r\n
\ =\r\n 0\r\n
\ \r\n \r\n
\ , then any such solution is global
and bounded, that\r\n \r\n \r\n •\r\n
\ if \r\n \r\n
\ \r\n \r\n \r\n
\ lim sup\r\n
\ \r\n ξ\r\n
\ →\r\n
\ ∞\r\n
\ \r\n \r\n
\ I\r\n (\r\n ξ\r\n
\ )\r\n
\ <\r\n ∞\r\n \r\n
\ \r\n
and \r\n \r\n
\ \r\n \r\n \r\n
\ ∫\r\n Ω\r\n \r\n
\ \r\n u\r\n
\ 0\r\n \r\n
\ \r\n \r\n
\ is suitably small, then the
corresponding solution is global and bounded, and that\r\n \r\n
\ \r\n •\r\n
\ if \r\n \r\n
\ \r\n \r\n \r\n
\ lim inf\r\n
\ \r\n ξ\r\n
\ →\r\n
\ ∞\r\n
\ \r\n \r\n
\ I\r\n (\r\n ξ\r\n
\ )\r\n
\ >\r\n 0\r\n
\ \r\n \r\n
\ , then at each appropriately
large mass level m, there exist radial initial data
u\r\n 0
such that \r\n \r\n
\ \r\n \r\n \r\n
\ ∫\r\n Ω\r\n \r\n
\ \r\n u\r\n
\ 0\r\n \r\n
\ =\r\n m\r\n
\ \r\n \r\n
\ , and that the associated solution
blows up either in finite or in infinite time.\r\n \r\n
\ \r\n \r\n This
especially reveals the presence of critical mass phenomena whenever \r\n
\ \r\n \r\n \r\n \r\n
\ lim\r\n
\ \r\n ξ\r\n
\ →\r\n
\ ∞\r\n
\ \r\n \r\n
\ I\r\n (\r\n ξ\r\n
\ )\r\n ∈\r\n
\ (\r\n 0\r\n
\ ,\r\n ∞\r\n )\r\n
\ \r\n \r\n
exists."
article_number: '125006'
author:
- first_name: Mengyao
full_name: Ding, Mengyao
last_name: Ding
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
citation:
ama: 'Ding M, Winkler M. Radial blow-up in quasilinear Keller-Segel systems: approaching
the full picture. Nonlinearity. 2024;37(12). doi:10.1088/1361-6544/ad871a'
apa: 'Ding, M., & Winkler, M. (2024). Radial blow-up in quasilinear Keller-Segel
systems: approaching the full picture. Nonlinearity, 37(12), Article
125006. https://doi.org/10.1088/1361-6544/ad871a'
bibtex: '@article{Ding_Winkler_2024, title={Radial blow-up in quasilinear Keller-Segel
systems: approaching the full picture}, volume={37}, DOI={10.1088/1361-6544/ad871a},
number={12125006}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Ding,
Mengyao and Winkler, Michael}, year={2024} }'
chicago: 'Ding, Mengyao, and Michael Winkler. “Radial Blow-up in Quasilinear Keller-Segel
Systems: Approaching the Full Picture.” Nonlinearity 37, no. 12 (2024).
https://doi.org/10.1088/1361-6544/ad871a.'
ieee: 'M. Ding and M. Winkler, “Radial blow-up in quasilinear Keller-Segel systems:
approaching the full picture,” Nonlinearity, vol. 37, no. 12, Art. no.
125006, 2024, doi: 10.1088/1361-6544/ad871a.'
mla: 'Ding, Mengyao, and Michael Winkler. “Radial Blow-up in Quasilinear Keller-Segel
Systems: Approaching the Full Picture.” Nonlinearity, vol. 37, no. 12,
125006, IOP Publishing, 2024, doi:10.1088/1361-6544/ad871a.'
short: M. Ding, M. Winkler, Nonlinearity 37 (2024).
date_created: 2025-12-18T19:04:45Z
date_updated: 2025-12-18T20:13:49Z
doi: 10.1088/1361-6544/ad871a
intvolume: ' 37'
issue: '12'
language:
- iso: eng
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
status: public
title: 'Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture'
type: journal_article
user_id: '31496'
volume: 37
year: '2024'
...
---
_id: '53345'
abstract:
- lang: eng
text: 'AbstractA no-flux initial-boundary value
problem forut=Δ(uϕ(v)),vt=Δv−uv,(⋆)is considered
in smoothly bounded subdomains ofRnwithn⩾1and suitably regular initial data, whereφis
assumed to reflect algebraic type cross-degeneracies by sharing essential features
with0⩽ξ↦ξαfor someα⩾1. Based on the discovery of a gradient structure acting
at regularity levels mild enough to be consistent with degeneracy-driven limitations
of smoothness information, in this general setting it is shown that with some
measurable limit profileu∞and
some null setN⋆⊂(0,∞),
a corresponding global generalized solution, known to exist according to recent
literature, satisfiesρ(u(⋅,t))⇀⋆ρ(u∞)in L∞(Ω) and v(⋅,t)→0in Lp(Ω)for
all p⩾1as(0,∞)∖N⋆∋t→∞, whereρ(ξ):=ξ2(ξ+1)2,ξ⩾0. In the particular case when eithern⩽2andα⩾1is arbitrary, orn⩾1andα∈[1,2],
additional quantitative information on the deviation of trajectories from the
initial data is derived. This is found to imply a lower estimate for the spatial
oscillation of the respective first components throughout evolution, and moreover
this is seen to entail that each of the uncountably many steady states(u⋆,0)of
(⋆) is stable with respect to a suitably chosen norm topology.'
author:
- first_name: Michael
full_name: Winkler, Michael
last_name: Winkler
citation:
ama: Winkler M. Stabilization despite pervasive strong cross-degeneracies in a nonlinear
diffusion model for migration–consumption interaction. Nonlinearity. 2023;36(8):4438-4469.
doi:10.1088/1361-6544/ace22e
apa: Winkler, M. (2023). Stabilization despite pervasive strong cross-degeneracies
in a nonlinear diffusion model for migration–consumption interaction. Nonlinearity,
36(8), 4438–4469. https://doi.org/10.1088/1361-6544/ace22e
bibtex: '@article{Winkler_2023, title={Stabilization despite pervasive strong cross-degeneracies
in a nonlinear diffusion model for migration–consumption interaction}, volume={36},
DOI={10.1088/1361-6544/ace22e},
number={8}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Winkler,
Michael}, year={2023}, pages={4438–4469} }'
chicago: 'Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies
in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” Nonlinearity
36, no. 8 (2023): 4438–69. https://doi.org/10.1088/1361-6544/ace22e.'
ieee: 'M. Winkler, “Stabilization despite pervasive strong cross-degeneracies in
a nonlinear diffusion model for migration–consumption interaction,” Nonlinearity,
vol. 36, no. 8, pp. 4438–4469, 2023, doi: 10.1088/1361-6544/ace22e.'
mla: Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies
in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” Nonlinearity,
vol. 36, no. 8, IOP Publishing, 2023, pp. 4438–69, doi:10.1088/1361-6544/ace22e.
short: M. Winkler, Nonlinearity 36 (2023) 4438–4469.
date_created: 2024-04-07T12:56:35Z
date_updated: 2024-04-07T12:56:40Z
doi: 10.1088/1361-6544/ace22e
intvolume: ' 36'
issue: '8'
keyword:
- Applied Mathematics
- General Physics and Astronomy
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 4438-4469
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
status: public
title: Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion
model for migration–consumption interaction
type: journal_article
user_id: '31496'
volume: 36
year: '2023'
...
---
_id: '63281'
abstract:
- lang: eng
text: AbstractA no-flux initial-boundary value
problem forut=Δ(uϕ(v)),vt=Δv−uv,(⋆)is considered
in smoothly bounded subdomains ofRnwithn⩾1and
suitably regular initial data, whereφis assumed to
reflect algebraic type cross-degeneracies by sharing essential features with0⩽ξ↦ξαfor
someα⩾1.
Based on the discovery of a gradient structure acting at regularity levels mild
enough to be consistent with degeneracy-driven limitations of smoothness information,
in this general setting it is shown that with some measurable limit profileu∞and
some null setN⋆⊂(0,∞), a
corresponding global generalized solution, known to exist according to recent
literature, satisfiesρ(u(⋅,t))⇀⋆ρ(u∞)in L∞(Ω) and v(⋅,t)→0in Lp(Ω)for
all p⩾1as(0,∞)∖N⋆∋t→∞,
whereρ(ξ):=ξ2(ξ+1)2,ξ⩾0.
In the particular case when eithern⩽2andα⩾1is
arbitrary, orn⩾1andα∈[1,2],
additional quantitative information on the deviation of trajectories from the
initial data is derived. This is found to imply a lower estimate for the spatial
oscillation of the respective first components throughout evolution, and moreover
this is seen to entail that each of the uncountably many steady states(u⋆,0)of
(⋆)
is stable with respect to a suitably chosen norm topology.
author:
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
citation:
ama: Winkler M. Stabilization despite pervasive strong cross-degeneracies in a nonlinear
diffusion model for migration–consumption interaction. Nonlinearity. 2023;36(8):4438-4469.
doi:10.1088/1361-6544/ace22e
apa: Winkler, M. (2023). Stabilization despite pervasive strong cross-degeneracies
in a nonlinear diffusion model for migration–consumption interaction. Nonlinearity,
36(8), 4438–4469. https://doi.org/10.1088/1361-6544/ace22e
bibtex: '@article{Winkler_2023, title={Stabilization despite pervasive strong cross-degeneracies
in a nonlinear diffusion model for migration–consumption interaction}, volume={36},
DOI={10.1088/1361-6544/ace22e},
number={8}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Winkler,
Michael}, year={2023}, pages={4438–4469} }'
chicago: 'Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies
in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” Nonlinearity
36, no. 8 (2023): 4438–69. https://doi.org/10.1088/1361-6544/ace22e.'
ieee: 'M. Winkler, “Stabilization despite pervasive strong cross-degeneracies in
a nonlinear diffusion model for migration–consumption interaction,” Nonlinearity,
vol. 36, no. 8, pp. 4438–4469, 2023, doi: 10.1088/1361-6544/ace22e.'
mla: Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies
in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” Nonlinearity,
vol. 36, no. 8, IOP Publishing, 2023, pp. 4438–69, doi:10.1088/1361-6544/ace22e.
short: M. Winkler, Nonlinearity 36 (2023) 4438–4469.
date_created: 2025-12-18T19:17:01Z
date_updated: 2025-12-18T20:12:06Z
doi: 10.1088/1361-6544/ace22e
intvolume: ' 36'
issue: '8'
language:
- iso: eng
page: 4438-4469
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
status: public
title: Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion
model for migration–consumption interaction
type: journal_article
user_id: '31496'
volume: 36
year: '2023'
...
---
_id: '33264'
abstract:
- lang: eng
text: We investigate bifurcations in feedforward coupled cell networks. Feedforward
structure (the absence of feedback) can be defined by a partial order on the cells.
We use this property to study generic one-parameter steady state bifurcations
for such networks. Branching solutions and their asymptotics are described in
terms of Taylor coefficients of the internal dynamics. They can be determined
via an algorithm that only exploits the network structure. Similar to previous
results on feedforward chains, we observe amplifications of the growth rates of
steady state branches induced by the feedforward structure. However, contrary
to these earlier results, as the interaction scenarios can be more complicated
in general feedforward networks, different branching patterns and different amplifications
can occur for different regions in the space of Taylor coefficients.
author:
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Eddie
full_name: Nijholt, Eddie
last_name: Nijholt
- first_name: Bob
full_name: Rink, Bob
last_name: Rink
citation:
ama: von der Gracht S, Nijholt E, Rink B. Amplified steady state bifurcations in
feedforward networks. Nonlinearity. 2022;35(4):2073-2120. doi:10.1088/1361-6544/ac5463
apa: von der Gracht, S., Nijholt, E., & Rink, B. (2022). Amplified steady state
bifurcations in feedforward networks. Nonlinearity, 35(4), 2073–2120.
https://doi.org/10.1088/1361-6544/ac5463
bibtex: '@article{von der Gracht_Nijholt_Rink_2022, title={Amplified steady state
bifurcations in feedforward networks}, volume={35}, DOI={10.1088/1361-6544/ac5463},
number={4}, journal={Nonlinearity}, publisher={IOP Publishing}, author={von der
Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2022}, pages={2073–2120}
}'
chicago: 'Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Amplified Steady
State Bifurcations in Feedforward Networks.” Nonlinearity 35, no. 4 (2022):
2073–2120. https://doi.org/10.1088/1361-6544/ac5463.'
ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Amplified steady state bifurcations
in feedforward networks,” Nonlinearity, vol. 35, no. 4, pp. 2073–2120,
2022, doi: 10.1088/1361-6544/ac5463.'
mla: von der Gracht, Sören, et al. “Amplified Steady State Bifurcations in Feedforward
Networks.” Nonlinearity, vol. 35, no. 4, IOP Publishing, 2022, pp. 2073–120,
doi:10.1088/1361-6544/ac5463.
short: S. von der Gracht, E. Nijholt, B. Rink, Nonlinearity 35 (2022) 2073–2120.
date_created: 2022-09-06T11:38:15Z
date_updated: 2022-09-07T08:36:46Z
doi: 10.1088/1361-6544/ac5463
extern: '1'
external_id:
arxiv:
- '2105.02547'
intvolume: ' 35'
issue: '4'
keyword:
- Applied Mathematics
- General Physics and Astronomy
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 2073-2120
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
status: public
title: Amplified steady state bifurcations in feedforward networks
type: journal_article
user_id: '97359'
volume: 35
year: '2022'
...
---
_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: '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: '8755'
abstract:
- lang: eng
text: Dynamic mode decomposition (DMD) is a recently developed tool for the analysis
of the behavior of complex dynamical systems. In this paper, we will propose an
extension of DMD that exploits low-rank tensor decompositions of potentially high-dimensional
data sets to compute the corresponding DMD modes and eigenvalues. The goal is
to reduce the computational complexity and also the amount of memory required
to store the data in order to mitigate the curse of dimensionality. The efficiency
of these tensor-based methods will be illustrated with the aid of several different
fluid dynamics problems such as the von Kármán vortex street and the simulation
of two merging vortices.
article_type: original
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Patrick
full_name: Gelß, Patrick
last_name: Gelß
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Christof
full_name: Schütte, Christof
last_name: Schütte
citation:
ama: Klus S, Gelß P, Peitz S, Schütte C. Tensor-based dynamic mode decomposition.
Nonlinearity. 2018;31(7):3359-3380. doi:10.1088/1361-6544/aabc8f
apa: Klus, S., Gelß, P., Peitz, S., & Schütte, C. (2018). Tensor-based dynamic
mode decomposition. Nonlinearity, 31(7), 3359–3380. https://doi.org/10.1088/1361-6544/aabc8f
bibtex: '@article{Klus_Gelß_Peitz_Schütte_2018, title={Tensor-based dynamic mode
decomposition}, volume={31}, DOI={10.1088/1361-6544/aabc8f},
number={7}, journal={Nonlinearity}, author={Klus, Stefan and Gelß, Patrick and
Peitz, Sebastian and Schütte, Christof}, year={2018}, pages={3359–3380} }'
chicago: 'Klus, Stefan, Patrick Gelß, Sebastian Peitz, and Christof Schütte. “Tensor-Based
Dynamic Mode Decomposition.” Nonlinearity 31, no. 7 (2018): 3359–80. https://doi.org/10.1088/1361-6544/aabc8f.'
ieee: S. Klus, P. Gelß, S. Peitz, and C. Schütte, “Tensor-based dynamic mode decomposition,”
Nonlinearity, vol. 31, no. 7, pp. 3359–3380, 2018.
mla: Klus, Stefan, et al. “Tensor-Based Dynamic Mode Decomposition.” Nonlinearity,
vol. 31, no. 7, 2018, pp. 3359–80, doi:10.1088/1361-6544/aabc8f.
short: S. Klus, P. Gelß, S. Peitz, C. Schütte, Nonlinearity 31 (2018) 3359–3380.
date_created: 2019-03-29T13:32:04Z
date_updated: 2022-01-06T07:04:00Z
department:
- _id: '101'
doi: 10.1088/1361-6544/aabc8f
intvolume: ' 31'
issue: '7'
language:
- iso: eng
page: 3359-3380
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: Tensor-based dynamic mode decomposition
type: journal_article
user_id: '47427'
volume: 31
year: '2018'
...
---
_id: '63370'
author:
- first_name: Elio
full_name: Espejo, Elio
last_name: Espejo
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
citation:
ama: Espejo E, Winkler M. Global classical solvability and stabilization in a two-dimensional
chemotaxis-Navier–Stokes system modeling coral fertilization. Nonlinearity.
2018;31(4):1227-1259. doi:10.1088/1361-6544/aa9d5f
apa: Espejo, E., & Winkler, M. (2018). Global classical solvability and stabilization
in a two-dimensional chemotaxis-Navier–Stokes system modeling coral fertilization.
Nonlinearity, 31(4), 1227–1259. https://doi.org/10.1088/1361-6544/aa9d5f
bibtex: '@article{Espejo_Winkler_2018, title={Global classical solvability and stabilization
in a two-dimensional chemotaxis-Navier–Stokes system modeling coral fertilization},
volume={31}, DOI={10.1088/1361-6544/aa9d5f},
number={4}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Espejo,
Elio and Winkler, Michael}, year={2018}, pages={1227–1259} }'
chicago: 'Espejo, Elio, and Michael Winkler. “Global Classical Solvability and Stabilization
in a Two-Dimensional Chemotaxis-Navier–Stokes System Modeling Coral Fertilization.”
Nonlinearity 31, no. 4 (2018): 1227–59. https://doi.org/10.1088/1361-6544/aa9d5f.'
ieee: 'E. Espejo and M. Winkler, “Global classical solvability and stabilization
in a two-dimensional chemotaxis-Navier–Stokes system modeling coral fertilization,”
Nonlinearity, vol. 31, no. 4, pp. 1227–1259, 2018, doi: 10.1088/1361-6544/aa9d5f.'
mla: Espejo, Elio, and Michael Winkler. “Global Classical Solvability and Stabilization
in a Two-Dimensional Chemotaxis-Navier–Stokes System Modeling Coral Fertilization.”
Nonlinearity, vol. 31, no. 4, IOP Publishing, 2018, pp. 1227–59, doi:10.1088/1361-6544/aa9d5f.
short: E. Espejo, M. Winkler, Nonlinearity 31 (2018) 1227–1259.
date_created: 2025-12-19T11:03:26Z
date_updated: 2025-12-19T11:03:32Z
doi: 10.1088/1361-6544/aa9d5f
intvolume: ' 31'
issue: '4'
language:
- iso: eng
page: 1227-1259
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
status: public
title: Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier–Stokes
system modeling coral fertilization
type: journal_article
user_id: '31496'
volume: 31
year: '2018'
...
---
_id: '63376'
author:
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
citation:
ama: Winkler M. A critical blow-up exponent in a chemotaxis system with nonlinear
signal production. Nonlinearity. 2018;31(5):2031-2056. doi:10.1088/1361-6544/aaaa0e
apa: Winkler, M. (2018). A critical blow-up exponent in a chemotaxis system with
nonlinear signal production. Nonlinearity, 31(5), 2031–2056. https://doi.org/10.1088/1361-6544/aaaa0e
bibtex: '@article{Winkler_2018, title={A critical blow-up exponent in a chemotaxis
system with nonlinear signal production}, volume={31}, DOI={10.1088/1361-6544/aaaa0e},
number={5}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Winkler,
Michael}, year={2018}, pages={2031–2056} }'
chicago: 'Winkler, Michael. “A Critical Blow-up Exponent in a Chemotaxis System
with Nonlinear Signal Production.” Nonlinearity 31, no. 5 (2018): 2031–56.
https://doi.org/10.1088/1361-6544/aaaa0e.'
ieee: 'M. Winkler, “A critical blow-up exponent in a chemotaxis system with nonlinear
signal production,” Nonlinearity, vol. 31, no. 5, pp. 2031–2056, 2018,
doi: 10.1088/1361-6544/aaaa0e.'
mla: Winkler, Michael. “A Critical Blow-up Exponent in a Chemotaxis System with
Nonlinear Signal Production.” Nonlinearity, vol. 31, no. 5, IOP Publishing,
2018, pp. 2031–56, doi:10.1088/1361-6544/aaaa0e.
short: M. Winkler, Nonlinearity 31 (2018) 2031–2056.
date_created: 2025-12-19T11:06:33Z
date_updated: 2025-12-19T11:06:40Z
doi: 10.1088/1361-6544/aaaa0e
intvolume: ' 31'
issue: '5'
language:
- iso: eng
page: 2031-2056
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
status: public
title: A critical blow-up exponent in a chemotaxis system with nonlinear signal production
type: journal_article
user_id: '31496'
volume: 31
year: '2018'
...
---
_id: '34659'
author:
- first_name: Tobias
full_name: Black, Tobias
id: '23686'
last_name: Black
orcid: 0000-0001-9963-0800
citation:
ama: Black T. Blow-up of weak solutions to a chemotaxis system under influence of
an external chemoattractant. Nonlinearity. 2016;29(6):1865-1886. doi:10.1088/0951-7715/29/6/1865
apa: Black, T. (2016). Blow-up of weak solutions to a chemotaxis system under influence
of an external chemoattractant. Nonlinearity, 29(6), 1865–1886.
https://doi.org/10.1088/0951-7715/29/6/1865
bibtex: '@article{Black_2016, title={Blow-up of weak solutions to a chemotaxis system
under influence of an external chemoattractant}, volume={29}, DOI={10.1088/0951-7715/29/6/1865},
number={6}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Black,
Tobias}, year={2016}, pages={1865–1886} }'
chicago: 'Black, Tobias. “Blow-up of Weak Solutions to a Chemotaxis System under
Influence of an External Chemoattractant.” Nonlinearity 29, no. 6 (2016):
1865–86. https://doi.org/10.1088/0951-7715/29/6/1865.'
ieee: 'T. Black, “Blow-up of weak solutions to a chemotaxis system under influence
of an external chemoattractant,” Nonlinearity, vol. 29, no. 6, pp. 1865–1886,
2016, doi: 10.1088/0951-7715/29/6/1865.'
mla: Black, Tobias. “Blow-up of Weak Solutions to a Chemotaxis System under Influence
of an External Chemoattractant.” Nonlinearity, vol. 29, no. 6, IOP Publishing,
2016, pp. 1865–86, doi:10.1088/0951-7715/29/6/1865.
short: T. Black, Nonlinearity 29 (2016) 1865–1886.
date_created: 2022-12-21T09:46:00Z
date_updated: 2022-12-21T10:05:45Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
doi: 10.1088/0951-7715/29/6/1865
intvolume: ' 29'
issue: '6'
keyword:
- Applied Mathematics
- General Physics and Astronomy
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 1865-1886
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
status: public
title: Blow-up of weak solutions to a chemotaxis system under influence of an external
chemoattractant
type: journal_article
user_id: '23686'
volume: 29
year: '2016'
...
---
_id: '26511'
author:
- first_name: Sonja
full_name: Barkhofen, Sonja
id: '48188'
last_name: Barkhofen
- first_name: F
full_name: Faure, F
last_name: Faure
- first_name: T
full_name: Weich, T
last_name: Weich
citation:
ama: Barkhofen S, Faure F, Weich T. Resonance chains in open systems, generalized
zeta functions and clustering of the length spectrum. Nonlinearity. Published
online 2014:1829-1858. doi:10.1088/0951-7715/27/8/1829
apa: Barkhofen, S., Faure, F., & Weich, T. (2014). Resonance chains in open
systems, generalized zeta functions and clustering of the length spectrum. Nonlinearity,
1829–1858. https://doi.org/10.1088/0951-7715/27/8/1829
bibtex: '@article{Barkhofen_Faure_Weich_2014, title={Resonance chains in open systems,
generalized zeta functions and clustering of the length spectrum}, DOI={10.1088/0951-7715/27/8/1829},
journal={Nonlinearity}, author={Barkhofen, Sonja and Faure, F and Weich, T}, year={2014},
pages={1829–1858} }'
chicago: Barkhofen, Sonja, F Faure, and T Weich. “Resonance Chains in Open Systems,
Generalized Zeta Functions and Clustering of the Length Spectrum.” Nonlinearity,
2014, 1829–58. https://doi.org/10.1088/0951-7715/27/8/1829.
ieee: 'S. Barkhofen, F. Faure, and T. Weich, “Resonance chains in open systems,
generalized zeta functions and clustering of the length spectrum,” Nonlinearity,
pp. 1829–1858, 2014, doi: 10.1088/0951-7715/27/8/1829.'
mla: Barkhofen, Sonja, et al. “Resonance Chains in Open Systems, Generalized Zeta
Functions and Clustering of the Length Spectrum.” Nonlinearity, 2014, pp.
1829–58, doi:10.1088/0951-7715/27/8/1829.
short: S. Barkhofen, F. Faure, T. Weich, Nonlinearity (2014) 1829–1858.
date_created: 2021-10-19T07:14:45Z
date_updated: 2022-01-06T06:57:21Z
doi: 10.1088/0951-7715/27/8/1829
language:
- iso: eng
page: 1829-1858
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: Resonance chains in open systems, generalized zeta functions and clustering
of the length spectrum
type: journal_article
user_id: '48188'
year: '2014'
...
---
_id: '31296'
author:
- first_name: Sonja
full_name: Barkhofen, Sonja
id: '48188'
last_name: Barkhofen
- first_name: F
full_name: Faure, F
last_name: Faure
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
citation:
ama: Barkhofen S, Faure F, Weich T. Resonance chains in open systems, generalized
zeta functions and clustering of the length spectrum. Nonlinearity. 2014;27(8):1829-1858.
doi:10.1088/0951-7715/27/8/1829
apa: Barkhofen, S., Faure, F., & Weich, T. (2014). Resonance chains in open
systems, generalized zeta functions and clustering of the length spectrum. Nonlinearity,
27(8), 1829–1858. https://doi.org/10.1088/0951-7715/27/8/1829
bibtex: '@article{Barkhofen_Faure_Weich_2014, title={Resonance chains in open systems,
generalized zeta functions and clustering of the length spectrum}, volume={27},
DOI={10.1088/0951-7715/27/8/1829},
number={8}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Barkhofen,
Sonja and Faure, F and Weich, Tobias}, year={2014}, pages={1829–1858} }'
chicago: 'Barkhofen, Sonja, F Faure, and Tobias Weich. “Resonance Chains in Open
Systems, Generalized Zeta Functions and Clustering of the Length Spectrum.” Nonlinearity
27, no. 8 (2014): 1829–58. https://doi.org/10.1088/0951-7715/27/8/1829.'
ieee: 'S. Barkhofen, F. Faure, and T. Weich, “Resonance chains in open systems,
generalized zeta functions and clustering of the length spectrum,” Nonlinearity,
vol. 27, no. 8, pp. 1829–1858, 2014, doi: 10.1088/0951-7715/27/8/1829.'
mla: Barkhofen, Sonja, et al. “Resonance Chains in Open Systems, Generalized Zeta
Functions and Clustering of the Length Spectrum.” Nonlinearity, vol. 27,
no. 8, IOP Publishing, 2014, pp. 1829–58, doi:10.1088/0951-7715/27/8/1829.
short: S. Barkhofen, F. Faure, T. Weich, Nonlinearity 27 (2014) 1829–1858.
date_created: 2022-05-17T12:58:25Z
date_updated: 2023-01-19T08:56:12Z
department:
- _id: '10'
- _id: '548'
- _id: '288'
doi: 10.1088/0951-7715/27/8/1829
external_id:
arxiv:
- '1403.7771 '
intvolume: ' 27'
issue: '8'
keyword:
- Applied Mathematics
- General Physics and Astronomy
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 1829-1858
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
status: public
title: Resonance chains in open systems, generalized zeta functions and clustering
of the length spectrum
type: journal_article
user_id: '48188'
volume: 27
year: '2014'
...
---
_id: '16554'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
- first_name: Stefan
full_name: Sertl, Stefan
last_name: Sertl
citation:
ama: Dellnitz M, Froyland G, Sertl S. On the isolated spectrum of the Perron-Frobenius
operator. Nonlinearity. 2000:1171-1188. doi:10.1088/0951-7715/13/4/310
apa: Dellnitz, M., Froyland, G., & Sertl, S. (2000). On the isolated spectrum
of the Perron-Frobenius operator. Nonlinearity, 1171–1188. https://doi.org/10.1088/0951-7715/13/4/310
bibtex: '@article{Dellnitz_Froyland_Sertl_2000, title={On the isolated spectrum
of the Perron-Frobenius operator}, DOI={10.1088/0951-7715/13/4/310},
journal={Nonlinearity}, author={Dellnitz, Michael and Froyland, Gary and Sertl,
Stefan}, year={2000}, pages={1171–1188} }'
chicago: Dellnitz, Michael, Gary Froyland, and Stefan Sertl. “On the Isolated Spectrum
of the Perron-Frobenius Operator.” Nonlinearity, 2000, 1171–88. https://doi.org/10.1088/0951-7715/13/4/310.
ieee: M. Dellnitz, G. Froyland, and S. Sertl, “On the isolated spectrum of the Perron-Frobenius
operator,” Nonlinearity, pp. 1171–1188, 2000.
mla: Dellnitz, Michael, et al. “On the Isolated Spectrum of the Perron-Frobenius
Operator.” Nonlinearity, 2000, pp. 1171–88, doi:10.1088/0951-7715/13/4/310.
short: M. Dellnitz, G. Froyland, S. Sertl, Nonlinearity (2000) 1171–1188.
date_created: 2020-04-15T09:09:46Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1088/0951-7715/13/4/310
language:
- iso: eng
page: 1171-1188
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: On the isolated spectrum of the Perron-Frobenius operator
type: journal_article
user_id: '15701'
year: '2000'
...
---
_id: '16532'
author:
- first_name: M
full_name: Dellnitz, M
last_name: Dellnitz
- first_name: C
full_name: Heinrich, C
last_name: Heinrich
citation:
ama: Dellnitz M, Heinrich C. Admissible symmetry increasing bifurcations. Nonlinearity.
1995:1039-1066. doi:10.1088/0951-7715/8/6/009
apa: Dellnitz, M., & Heinrich, C. (1995). Admissible symmetry increasing bifurcations.
Nonlinearity, 1039–1066. https://doi.org/10.1088/0951-7715/8/6/009
bibtex: '@article{Dellnitz_Heinrich_1995, title={Admissible symmetry increasing
bifurcations}, DOI={10.1088/0951-7715/8/6/009},
journal={Nonlinearity}, author={Dellnitz, M and Heinrich, C}, year={1995}, pages={1039–1066}
}'
chicago: Dellnitz, M, and C Heinrich. “Admissible Symmetry Increasing Bifurcations.”
Nonlinearity, 1995, 1039–66. https://doi.org/10.1088/0951-7715/8/6/009.
ieee: M. Dellnitz and C. Heinrich, “Admissible symmetry increasing bifurcations,”
Nonlinearity, pp. 1039–1066, 1995.
mla: Dellnitz, M., and C. Heinrich. “Admissible Symmetry Increasing Bifurcations.”
Nonlinearity, 1995, pp. 1039–66, doi:10.1088/0951-7715/8/6/009.
short: M. Dellnitz, C. Heinrich, Nonlinearity (1995) 1039–1066.
date_created: 2020-04-15T08:25:12Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1088/0951-7715/8/6/009
language:
- iso: eng
page: 1039-1066
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: Admissible symmetry increasing bifurcations
type: journal_article
user_id: '15701'
year: '1995'
...
---
_id: '16542'
author:
- first_name: M
full_name: Dellnitz, M
last_name: Dellnitz
- first_name: I
full_name: Melbourne, I
last_name: Melbourne
citation:
ama: Dellnitz M, Melbourne I. A note on the shadowing lemma and symmetric periodic
points. Nonlinearity. 1995:1067-1075. doi:10.1088/0951-7715/8/6/010
apa: Dellnitz, M., & Melbourne, I. (1995). A note on the shadowing lemma and
symmetric periodic points. Nonlinearity, 1067–1075. https://doi.org/10.1088/0951-7715/8/6/010
bibtex: '@article{Dellnitz_Melbourne_1995, title={A note on the shadowing lemma
and symmetric periodic points}, DOI={10.1088/0951-7715/8/6/010},
journal={Nonlinearity}, author={Dellnitz, M and Melbourne, I}, year={1995}, pages={1067–1075}
}'
chicago: Dellnitz, M, and I Melbourne. “A Note on the Shadowing Lemma and Symmetric
Periodic Points.” Nonlinearity, 1995, 1067–75. https://doi.org/10.1088/0951-7715/8/6/010.
ieee: M. Dellnitz and I. Melbourne, “A note on the shadowing lemma and symmetric
periodic points,” Nonlinearity, pp. 1067–1075, 1995.
mla: Dellnitz, M., and I. Melbourne. “A Note on the Shadowing Lemma and Symmetric
Periodic Points.” Nonlinearity, 1995, pp. 1067–75, doi:10.1088/0951-7715/8/6/010.
short: M. Dellnitz, I. Melbourne, Nonlinearity (1995) 1067–1075.
date_created: 2020-04-15T08:46:30Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1088/0951-7715/8/6/010
language:
- iso: eng
page: 1067-1075
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: A note on the shadowing lemma and symmetric periodic points
type: journal_article
user_id: '15701'
year: '1995'
...
---
_id: '16548'
author:
- first_name: M
full_name: Dellnitz, M
last_name: Dellnitz
- first_name: I
full_name: Melbourne, I
last_name: Melbourne
- first_name: J E
full_name: Marsden, J E
last_name: Marsden
citation:
ama: Dellnitz M, Melbourne I, Marsden JE. Generic bifurcation of Hamiltonian vector
fields with symmetry. Nonlinearity. 1992:979-996. doi:10.1088/0951-7715/5/4/008
apa: Dellnitz, M., Melbourne, I., & Marsden, J. E. (1992). Generic bifurcation
of Hamiltonian vector fields with symmetry. Nonlinearity, 979–996. https://doi.org/10.1088/0951-7715/5/4/008
bibtex: '@article{Dellnitz_Melbourne_Marsden_1992, title={Generic bifurcation of
Hamiltonian vector fields with symmetry}, DOI={10.1088/0951-7715/5/4/008},
journal={Nonlinearity}, author={Dellnitz, M and Melbourne, I and Marsden, J E},
year={1992}, pages={979–996} }'
chicago: Dellnitz, M, I Melbourne, and J E Marsden. “Generic Bifurcation of Hamiltonian
Vector Fields with Symmetry.” Nonlinearity, 1992, 979–96. https://doi.org/10.1088/0951-7715/5/4/008.
ieee: M. Dellnitz, I. Melbourne, and J. E. Marsden, “Generic bifurcation of Hamiltonian
vector fields with symmetry,” Nonlinearity, pp. 979–996, 1992.
mla: Dellnitz, M., et al. “Generic Bifurcation of Hamiltonian Vector Fields with
Symmetry.” Nonlinearity, 1992, pp. 979–96, doi:10.1088/0951-7715/5/4/008.
short: M. Dellnitz, I. Melbourne, J.E. Marsden, Nonlinearity (1992) 979–996.
date_created: 2020-04-15T08:59:25Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1088/0951-7715/5/4/008
language:
- iso: eng
page: 979-996
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: Generic bifurcation of Hamiltonian vector fields with symmetry
type: journal_article
user_id: '15701'
year: '1992'
...