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Mathematics > Dynamical Systems

arXiv:1812.08727 (math)
[Submitted on 20 Dec 2018 (v1), last revised 11 Jul 2020 (this version, v3)]

Title:Recognition of symmetries in reversible maps

Authors:Patrícia H. Baptistelli, Isabel S. Labouriau, Miriam Manoel
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Abstract:We deal with germs of diffeomorphisms that are reversible under an involution. We establish that this condition implies that, in general, both the family of reversing symmetries and the group of symmetries are not finite, in contrast with continuous-time dynamics, where typically there are finitely many reversing symmetries. From this we obtain two chains of fixed-points subspaces of involutory reversing symmetries that we use to obtain geometric information on the discrete dynamics generated by a given diffeomorphism. The results are illustrated by the generic case in arbitrary dimension, when the diffeomorphism is the composition of transversal linear involutions.
Subjects: Dynamical Systems (math.DS)
MSC classes: 58J70
Cite as: arXiv:1812.08727 [math.DS]
  (or arXiv:1812.08727v3 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.1812.08727

Submission history

From: Isabel Salgado Labouriau [view email]
[v1] Thu, 20 Dec 2018 17:58:30 UTC (36 KB)
[v2] Thu, 14 May 2020 23:15:53 UTC (35 KB)
[v3] Sat, 11 Jul 2020 18:25:39 UTC (35 KB)
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