A Conley-type Lyapunov function for the strong chain recurrent set - Sorbonne Université
Journal Articles Topology and its Applications Year : 2022

A Conley-type Lyapunov function for the strong chain recurrent set

Abstract

Let φ : X × R → X be a continuous flow on a compact metric space (X, d). In this article we constructively prove the existence of a continuous Lyapunov function for φ which is strictly decreasing outside SCR d (φ). Such a result generalizes Conley's Fundamental Theorem of Dynamical Systems for the strong chain recurrent set.

Dates and versions

hal-03574220 , version 1 (15-02-2022)

Identifiers

Cite

Olga Bernardi, Anna Florio, Jim Wiseman. A Conley-type Lyapunov function for the strong chain recurrent set. Topology and its Applications, 2022, 307, pp.107768. ⟨10.1016/j.topol.2021.107768⟩. ⟨hal-03574220⟩
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