Shift dynamics near non-elementary T-points with real eigenvalues

Abstract

We consider non-elementary T-points in reversible systems in R 2n+1 . We assume that the leading eigenvalues are real. We prove the existence of shift dynamics in the unfolding of this T-point. Furthermore, we study local bifurcations of symmetric periodic orbits occurring in the process of dissolution of the chaotic dynamics.

Global bifurcations close to symmetry

“…Using the Lin's method, the authors extend the analysis to cycles in spaces of arbitrary dimension, while restricting it to trajectories that remain for all time inside a small tubular neighbourhood of the cycle. We also refer the reader to [32], where the authors consider non-elementary T -points in reversible differential equations. The leading eigenvalues at the two equilibria are real and the two-dimensional invariant manifolds meet tangentially.…”

“…For instance, Bykov in [10,11] addresses the case of different chirality without mentioning it explicitly -see a discussion in Section 7 of [36]. Cycles with the same chirality are treated in [3,34] and they occur naturally in reversible differential equations [32]. Dynamical features that are irrespective of chirality are described in [31].…”