---
_id: '16712'
abstract:
- lang: eng
text: We investigate self-adjoint matrices A∈Rn,n with respect to their equivariance
properties. We show in particular that a matrix is self-adjoint if and only if
it is equivariant with respect to the action of a group Γ2(A)⊂O(n) which is isomorphic
to ⊗nk=1Z2. If the self-adjoint matrix possesses multiple eigenvalues – this may,
for instance, be induced by symmetry properties of an underlying dynamical system
– then A is even equivariant with respect to the action of a group Γ(A)≃∏ki=1O(mi)
where m1,…,mk are the multiplicities of the eigenvalues λ1,…,λk of A. We discuss
implications of this result for equivariant bifurcation problems, and we briefly
address further applications for the Procrustes problem, graph symmetries and
Taylor expansions.
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
citation:
ama: Dellnitz M, Gebken B, Gerlach R, Klus S. On the equivariance properties of
self-adjoint matrices. Dynamical Systems. 2020;35(2):197-215. doi:10.1080/14689367.2019.1661355
apa: Dellnitz, M., Gebken, B., Gerlach, R., & Klus, S. (2020). On the equivariance
properties of self-adjoint matrices. Dynamical Systems, 35(2), 197–215.
https://doi.org/10.1080/14689367.2019.1661355
bibtex: '@article{Dellnitz_Gebken_Gerlach_Klus_2020, title={On the equivariance
properties of self-adjoint matrices}, volume={35}, DOI={10.1080/14689367.2019.1661355},
number={2}, journal={Dynamical Systems}, author={Dellnitz, Michael and Gebken,
Bennet and Gerlach, Raphael and Klus, Stefan}, year={2020}, pages={197–215} }'
chicago: 'Dellnitz, Michael, Bennet Gebken, Raphael Gerlach, and Stefan Klus. “On
the Equivariance Properties of Self-Adjoint Matrices.” Dynamical Systems
35, no. 2 (2020): 197–215. https://doi.org/10.1080/14689367.2019.1661355.'
ieee: 'M. Dellnitz, B. Gebken, R. Gerlach, and S. Klus, “On the equivariance properties
of self-adjoint matrices,” Dynamical Systems, vol. 35, no. 2, pp. 197–215,
2020, doi: 10.1080/14689367.2019.1661355.'
mla: Dellnitz, Michael, et al. “On the Equivariance Properties of Self-Adjoint Matrices.”
Dynamical Systems, vol. 35, no. 2, 2020, pp. 197–215, doi:10.1080/14689367.2019.1661355.
short: M. Dellnitz, B. Gebken, R. Gerlach, S. Klus, Dynamical Systems 35 (2020)
197–215.
date_created: 2020-04-16T14:07:25Z
date_updated: 2023-11-17T13:12:59Z
department:
- _id: '101'
doi: 10.1080/14689367.2019.1661355
intvolume: ' 35'
issue: '2'
language:
- iso: eng
main_file_link:
- url: https://doi.org/10.1080/14689367.2019.1661355
page: 197-215
publication: Dynamical Systems
publication_identifier:
issn:
- 1468-9367
- 1468-9375
publication_status: published
status: public
title: On the equivariance properties of self-adjoint matrices
type: journal_article
user_id: '32655'
volume: 35
year: '2020'
...
---
_id: '16540'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
citation:
ama: Dellnitz M, Klus S. Sensing and control in symmetric networks. Dynamical
Systems. 2017:61-79. doi:10.1080/14689367.2016.1215410
apa: Dellnitz, M., & Klus, S. (2017). Sensing and control in symmetric networks.
Dynamical Systems, 61–79. https://doi.org/10.1080/14689367.2016.1215410
bibtex: '@article{Dellnitz_Klus_2017, title={Sensing and control in symmetric networks},
DOI={10.1080/14689367.2016.1215410},
journal={Dynamical Systems}, author={Dellnitz, Michael and Klus, Stefan}, year={2017},
pages={61–79} }'
chicago: Dellnitz, Michael, and Stefan Klus. “Sensing and Control in Symmetric Networks.”
Dynamical Systems, 2017, 61–79. https://doi.org/10.1080/14689367.2016.1215410.
ieee: M. Dellnitz and S. Klus, “Sensing and control in symmetric networks,” Dynamical
Systems, pp. 61–79, 2017.
mla: Dellnitz, Michael, and Stefan Klus. “Sensing and Control in Symmetric Networks.”
Dynamical Systems, 2017, pp. 61–79, doi:10.1080/14689367.2016.1215410.
short: M. Dellnitz, S. Klus, Dynamical Systems (2017) 61–79.
date_created: 2020-04-15T08:40:29Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1080/14689367.2016.1215410
language:
- iso: eng
page: 61-79
publication: Dynamical Systems
publication_identifier:
issn:
- 1468-9367
- 1468-9375
publication_status: published
status: public
title: Sensing and control in symmetric networks
type: journal_article
user_id: '15701'
year: '2017'
...
---
_id: '33260'
abstract:
- lang: eng
text: In this paper we continue the study of group representations which are counterexamples
to the Ize conjecture. As in previous papers we find new infinite series of finite
groups leading to such counterexamples. These new series are quite different from
the previous ones, for example the group orders do not form an arithmetic progression.
However, as before we find Lie groups which contain all these groups. This additional
structure was observed, but not used in the previous studies of this problem.
Here we also investigate the related bifurcations. To a large extent, these are
closely related to the presence of mentioned compact Lie group containing the
finite groups. This might give a tool to study the bifurcations related to all
low dimensional counterexamples of the Ize conjecture. It also gives an indication
of where we can expect to find examples where the bifurcation behaviour is different
from what we have seen in the known examples.
author:
- first_name: Reiner
full_name: Lauterbach, Reiner
last_name: Lauterbach
- first_name: Sören
full_name: Schwenker, Sören
id: '97359'
last_name: Schwenker
orcid: 0000-0002-8054-2058
citation:
ama: Lauterbach R, Schwenker S. Equivariant bifurcations in four-dimensional fixed
point spaces. Dynamical Systems. 2016;32(1):117-147. doi:10.1080/14689367.2016.1219696
apa: Lauterbach, R., & Schwenker, S. (2016). Equivariant bifurcations in four-dimensional
fixed point spaces. Dynamical Systems, 32(1), 117–147. https://doi.org/10.1080/14689367.2016.1219696
bibtex: '@article{Lauterbach_Schwenker_2016, title={Equivariant bifurcations in
four-dimensional fixed point spaces}, volume={32}, DOI={10.1080/14689367.2016.1219696},
number={1}, journal={Dynamical Systems}, publisher={Informa UK Limited}, author={Lauterbach,
Reiner and Schwenker, Sören}, year={2016}, pages={117–147} }'
chicago: 'Lauterbach, Reiner, and Sören Schwenker. “Equivariant Bifurcations in
Four-Dimensional Fixed Point Spaces.” Dynamical Systems 32, no. 1 (2016):
117–47. https://doi.org/10.1080/14689367.2016.1219696.'
ieee: 'R. Lauterbach and S. Schwenker, “Equivariant bifurcations in four-dimensional
fixed point spaces,” Dynamical Systems, vol. 32, no. 1, pp. 117–147, 2016,
doi: 10.1080/14689367.2016.1219696.'
mla: Lauterbach, Reiner, and Sören Schwenker. “Equivariant Bifurcations in Four-Dimensional
Fixed Point Spaces.” Dynamical Systems, vol. 32, no. 1, Informa UK Limited,
2016, pp. 117–47, doi:10.1080/14689367.2016.1219696.
short: R. Lauterbach, S. Schwenker, Dynamical Systems 32 (2016) 117–147.
date_created: 2022-09-06T11:22:12Z
date_updated: 2022-09-07T08:33:36Z
doi: 10.1080/14689367.2016.1219696
extern: '1'
external_id:
arxiv:
- '1511.00545'
intvolume: ' 32'
issue: '1'
keyword:
- Computer Science Applications
- General Mathematics
language:
- iso: eng
page: 117-147
publication: Dynamical Systems
publication_identifier:
issn:
- 1468-9367
- 1468-9375
publication_status: published
publisher: Informa UK Limited
status: public
title: Equivariant bifurcations in four-dimensional fixed point spaces
type: journal_article
user_id: '97359'
volume: 32
year: '2016'
...
---
_id: '16617'
author:
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
citation:
ama: 'Junge O. An adaptive subdivision technique for the approximation of attractors
and invariant measures: proof of convergence. Dynamical Systems. 2001:213-222.
doi:10.1080/14689360109696233'
apa: 'Junge, O. (2001). An adaptive subdivision technique for the approximation
of attractors and invariant measures: proof of convergence. Dynamical Systems,
213–222. https://doi.org/10.1080/14689360109696233'
bibtex: '@article{Junge_2001, title={An adaptive subdivision technique for the approximation
of attractors and invariant measures: proof of convergence}, DOI={10.1080/14689360109696233},
journal={Dynamical Systems}, author={Junge, Oliver}, year={2001}, pages={213–222}
}'
chicago: 'Junge, Oliver. “An Adaptive Subdivision Technique for the Approximation
of Attractors and Invariant Measures: Proof of Convergence.” Dynamical Systems,
2001, 213–22. https://doi.org/10.1080/14689360109696233.'
ieee: 'O. Junge, “An adaptive subdivision technique for the approximation of attractors
and invariant measures: proof of convergence,” Dynamical Systems, pp. 213–222,
2001.'
mla: 'Junge, Oliver. “An Adaptive Subdivision Technique for the Approximation of
Attractors and Invariant Measures: Proof of Convergence.” Dynamical Systems,
2001, pp. 213–22, doi:10.1080/14689360109696233.'
short: O. Junge, Dynamical Systems (2001) 213–222.
date_created: 2020-04-16T08:09:10Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1080/14689360109696233
language:
- iso: eng
page: 213-222
publication: Dynamical Systems
publication_identifier:
issn:
- 1468-9367
- 1468-9375
publication_status: published
status: public
title: 'An adaptive subdivision technique for the approximation of attractors and
invariant measures: proof of convergence'
type: journal_article
user_id: '15701'
year: '2001'
...