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arXiv · 2011.09830

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

Olga Bernardi·Anna Florio·Jim Wiseman
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Abstract

Let $\phi:X\times\mathbb{R} \rightarrow X$ 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 $\phi$ which is strictly decreasing outside $\mathcal{SCR}_d(\phi)$. Such a result generalizes Conley's Fundamental Theorem of Dynamical Systems for the strong chain recurrent set.

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Olga Bernardi, Anna Florio, Jim Wiseman. 2020-11-19. A Conley-type Lyapunov function for the strong chain recurrent set. https://arxiv.org/abs/2011.09830

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