Symmetric homoclinic tangles in reversible dynamical systems have positive topological entropy

Autor:	Homburg, Ale Jan, Lamb, Jeroen, Turaev, Dmitry
Rok vydání:	2022
Předmět:	Mathematics - Dynamical Systems 34C37 37B40
Druh dokumentu:	Working Paper
Popis:	We consider reversible vector fields in $\mathbb{R}^{2n}$ such that the set of fixed points of the involutory reversing symmetry is $n$-dimensional. Let such system have a smooth one-parameter family of symmetric periodic orbits which is of saddle type in normal directions. We establish that topological entropy is positive when the stable and unstable manifolds of this family of periodic orbits have a strongly-transverse intersection. Comment: 24 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2207.10624 Zobrazit plný text záznamu View this record from Arxiv