The generalized recurrent set, explosions and Lyapunov functions - Avignon Université Access content directly
Journal Articles Journal of Dynamics and Differential Equations Year : 2020

The generalized recurrent set, explosions and Lyapunov functions

Abstract

We consider explosions in the generalized recurrent set for homeomorphisms on a compact metric space. We provide multiple examples to show that such explosions can occur, in contrast to the case for the chain recurrent set. We give sufficient conditions to avoid explosions and discuss their necessity. Moreover, we explain the relations between explosions and cycles for the generalized recurrent set. In particular, for a compact topological manifold with dimension greater or equal 2, we characterize explosion phenomena in terms of existence of cycles. We apply our results to give sufficient conditions for stability, under C 0 perturbations, of the property of admitting a continuous Lyapunov function which is not a first integral.
Fichier principal
Vignette du fichier
GR-explosions-Lyapunov-OB-AF-JW4.10.pdf (958.15 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02097706 , version 1 (12-04-2019)

Identifiers

  • HAL Id : hal-02097706 , version 1

Cite

Olga Bernardi, Anna Florio, Jim Wiseman. The generalized recurrent set, explosions and Lyapunov functions. Journal of Dynamics and Differential Equations, 2020. ⟨hal-02097706⟩
88 View
116 Download

Share

Gmail Facebook X LinkedIn More