--- _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' ...