[{"user_id":"32655","department":[{"_id":"101"}],"_id":"16712","language":[{"iso":"eng"}],"type":"journal_article","publication":"Dynamical Systems","status":"public","abstract":[{"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.","lang":"eng"}],"date_created":"2020-04-16T14:07:25Z","author":[{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"},{"first_name":"Bennet","last_name":"Gebken","id":"32643","full_name":"Gebken, Bennet"},{"last_name":"Gerlach","id":"32655","full_name":"Gerlach, Raphael","first_name":"Raphael"},{"first_name":"Stefan","last_name":"Klus","full_name":"Klus, Stefan"}],"volume":35,"date_updated":"2023-11-17T13:12:59Z","main_file_link":[{"url":"https://doi.org/10.1080/14689367.2019.1661355"}],"doi":"10.1080/14689367.2019.1661355","title":"On the equivariance properties of self-adjoint matrices","issue":"2","publication_status":"published","publication_identifier":{"issn":["1468-9367","1468-9375"]},"citation":{"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.","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} }","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>","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>.","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>"},"intvolume":"        35","page":"197-215","year":"2020"},{"status":"public","publication":"Dynamical Systems","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"101"}],"user_id":"15701","_id":"16540","page":"61-79","citation":{"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>","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>.","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} }","short":"M. Dellnitz, S. Klus, Dynamical Systems (2017) 61–79.","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>","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."},"year":"2017","publication_identifier":{"issn":["1468-9367","1468-9375"]},"publication_status":"published","doi":"10.1080/14689367.2016.1215410","title":"Sensing and control in symmetric networks","date_created":"2020-04-15T08:40:29Z","author":[{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"},{"first_name":"Stefan","full_name":"Klus, Stefan","last_name":"Klus"}],"date_updated":"2022-01-06T06:52:52Z"},{"page":"117-147","intvolume":"        32","citation":{"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} }","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.","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>","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>","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>.","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>."},"publication_identifier":{"issn":["1468-9367","1468-9375"]},"publication_status":"published","doi":"10.1080/14689367.2016.1219696","volume":32,"author":[{"first_name":"Reiner","last_name":"Lauterbach","full_name":"Lauterbach, Reiner"},{"id":"97359","full_name":"Schwenker, Sören","orcid":"0000-0002-8054-2058","last_name":"Schwenker","first_name":"Sören"}],"date_updated":"2022-09-07T08:33:36Z","status":"public","type":"journal_article","extern":"1","user_id":"97359","_id":"33260","year":"2016","issue":"1","title":"Equivariant bifurcations in four-dimensional fixed point spaces","date_created":"2022-09-06T11:22:12Z","publisher":"Informa UK Limited","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."}],"publication":"Dynamical Systems","language":[{"iso":"eng"}],"keyword":["Computer Science Applications","General Mathematics"],"external_id":{"arxiv":["1511.00545"]}},{"status":"public","type":"journal_article","publication":"Dynamical Systems","language":[{"iso":"eng"}],"user_id":"15701","department":[{"_id":"101"}],"_id":"16617","citation":{"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>","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>.","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} }","short":"O. Junge, Dynamical Systems (2001) 213–222.","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>","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."},"page":"213-222","year":"2001","publication_status":"published","publication_identifier":{"issn":["1468-9367","1468-9375"]},"doi":"10.1080/14689360109696233","title":"An adaptive subdivision technique for the approximation of attractors and invariant measures: proof of convergence","date_created":"2020-04-16T08:09:10Z","author":[{"first_name":"Oliver","last_name":"Junge","full_name":"Junge, Oliver"}],"date_updated":"2022-01-06T06:52:53Z"}]