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 SCRd(ϕ). Such a result generalizes Conley's Fundamental Theorem of Dynamical Systems for the strong chain recurrent set.
A Conley-type Lyapunov function for the strong chain recurrent set
Olga Bernardi
;
2022
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 SCRd(ϕ). Such a result generalizes Conley's Fundamental Theorem of Dynamical Systems for the strong chain recurrent set.
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