Recognition of symmetries in reversible maps

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:491

Article

Baptistelli, Patricia H.¹  Labouriau, Isabel S.^2,3  Manoel, Miriam⁴ 

[1] Univ Estadual Maringa, CCE, Dept Matemat, Av Colombo 5790, BR-87020900 Maringa, Parana, Brazil

[2] Univ Porto, Fac Ciencias, Ctr Matemat, Rua Campo Alegre 687, P-4169007 Porto, Portugal

[3] Univ Porto, Fac Ciencias, Dept Matemat, Rua Campo Alegre 687, P-4169007 Porto, Portugal

[4] Univ Sao Paulo, ICMC, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, Brazil

关键词: Reversible map;    Involutions;    Symmetry;    Fixed-point subspace;   

DOI  :  10.1016/j.jmaa.2020.124348

来源: Elsevier

【 摘 要 】

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. (C) 2020 Published by Elsevier Inc.

【 授权许可】

Free