---
_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. <i>Dynamical Systems</i>. 2020;35(2):197-215. doi:<a href="https://doi.org/10.1080/14689367.2019.1661355">10.1080/14689367.2019.1661355</a>
  apa: Dellnitz, M., Gebken, B., Gerlach, R., &#38; Klus, S. (2020). On the equivariance
    properties of self-adjoint matrices. <i>Dynamical Systems</i>, <i>35</i>(2), 197–215.
    <a href="https://doi.org/10.1080/14689367.2019.1661355">https://doi.org/10.1080/14689367.2019.1661355</a>
  bibtex: '@article{Dellnitz_Gebken_Gerlach_Klus_2020, title={On the equivariance
    properties of self-adjoint matrices}, volume={35}, DOI={<a href="https://doi.org/10.1080/14689367.2019.1661355">10.1080/14689367.2019.1661355</a>},
    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.” <i>Dynamical Systems</i>
    35, no. 2 (2020): 197–215. <a href="https://doi.org/10.1080/14689367.2019.1661355">https://doi.org/10.1080/14689367.2019.1661355</a>.'
  ieee: 'M. Dellnitz, B. Gebken, R. Gerlach, and S. Klus, “On the equivariance properties
    of self-adjoint matrices,” <i>Dynamical Systems</i>, vol. 35, no. 2, pp. 197–215,
    2020, doi: <a href="https://doi.org/10.1080/14689367.2019.1661355">10.1080/14689367.2019.1661355</a>.'
  mla: Dellnitz, Michael, et al. “On the Equivariance Properties of Self-Adjoint Matrices.”
    <i>Dynamical Systems</i>, vol. 35, no. 2, 2020, pp. 197–215, doi:<a href="https://doi.org/10.1080/14689367.2019.1661355">10.1080/14689367.2019.1661355</a>.
  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. <i>Dynamical
    Systems</i>. 2017:61-79. doi:<a href="https://doi.org/10.1080/14689367.2016.1215410">10.1080/14689367.2016.1215410</a>
  apa: Dellnitz, M., &#38; Klus, S. (2017). Sensing and control in symmetric networks.
    <i>Dynamical Systems</i>, 61–79. <a href="https://doi.org/10.1080/14689367.2016.1215410">https://doi.org/10.1080/14689367.2016.1215410</a>
  bibtex: '@article{Dellnitz_Klus_2017, title={Sensing and control in symmetric networks},
    DOI={<a href="https://doi.org/10.1080/14689367.2016.1215410">10.1080/14689367.2016.1215410</a>},
    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.”
    <i>Dynamical Systems</i>, 2017, 61–79. <a href="https://doi.org/10.1080/14689367.2016.1215410">https://doi.org/10.1080/14689367.2016.1215410</a>.
  ieee: M. Dellnitz and S. Klus, “Sensing and control in symmetric networks,” <i>Dynamical
    Systems</i>, pp. 61–79, 2017.
  mla: Dellnitz, Michael, and Stefan Klus. “Sensing and Control in Symmetric Networks.”
    <i>Dynamical Systems</i>, 2017, pp. 61–79, doi:<a href="https://doi.org/10.1080/14689367.2016.1215410">10.1080/14689367.2016.1215410</a>.
  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. <i>Dynamical Systems</i>. 2016;32(1):117-147. doi:<a href="https://doi.org/10.1080/14689367.2016.1219696">10.1080/14689367.2016.1219696</a>
  apa: Lauterbach, R., &#38; Schwenker, S. (2016). Equivariant bifurcations in four-dimensional
    fixed point spaces. <i>Dynamical Systems</i>, <i>32</i>(1), 117–147. <a href="https://doi.org/10.1080/14689367.2016.1219696">https://doi.org/10.1080/14689367.2016.1219696</a>
  bibtex: '@article{Lauterbach_Schwenker_2016, title={Equivariant bifurcations in
    four-dimensional fixed point spaces}, volume={32}, DOI={<a href="https://doi.org/10.1080/14689367.2016.1219696">10.1080/14689367.2016.1219696</a>},
    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.” <i>Dynamical Systems</i> 32, no. 1 (2016):
    117–47. <a href="https://doi.org/10.1080/14689367.2016.1219696">https://doi.org/10.1080/14689367.2016.1219696</a>.'
  ieee: 'R. Lauterbach and S. Schwenker, “Equivariant bifurcations in four-dimensional
    fixed point spaces,” <i>Dynamical Systems</i>, vol. 32, no. 1, pp. 117–147, 2016,
    doi: <a href="https://doi.org/10.1080/14689367.2016.1219696">10.1080/14689367.2016.1219696</a>.'
  mla: Lauterbach, Reiner, and Sören Schwenker. “Equivariant Bifurcations in Four-Dimensional
    Fixed Point Spaces.” <i>Dynamical Systems</i>, vol. 32, no. 1, Informa UK Limited,
    2016, pp. 117–47, doi:<a href="https://doi.org/10.1080/14689367.2016.1219696">10.1080/14689367.2016.1219696</a>.
  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. <i>Dynamical Systems</i>. 2001:213-222.
    doi:<a href="https://doi.org/10.1080/14689360109696233">10.1080/14689360109696233</a>'
  apa: 'Junge, O. (2001). An adaptive subdivision technique for the approximation
    of attractors and invariant measures: proof of convergence. <i>Dynamical Systems</i>,
    213–222. <a href="https://doi.org/10.1080/14689360109696233">https://doi.org/10.1080/14689360109696233</a>'
  bibtex: '@article{Junge_2001, title={An adaptive subdivision technique for the approximation
    of attractors and invariant measures: proof of convergence}, DOI={<a href="https://doi.org/10.1080/14689360109696233">10.1080/14689360109696233</a>},
    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.” <i>Dynamical Systems</i>,
    2001, 213–22. <a href="https://doi.org/10.1080/14689360109696233">https://doi.org/10.1080/14689360109696233</a>.'
  ieee: 'O. Junge, “An adaptive subdivision technique for the approximation of attractors
    and invariant measures: proof of convergence,” <i>Dynamical Systems</i>, pp. 213–222,
    2001.'
  mla: 'Junge, Oliver. “An Adaptive Subdivision Technique for the Approximation of
    Attractors and Invariant Measures: Proof of Convergence.” <i>Dynamical Systems</i>,
    2001, pp. 213–22, doi:<a href="https://doi.org/10.1080/14689360109696233">10.1080/14689360109696233</a>.'
  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'
...