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

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

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...

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Veröffentlicht in:Topology and its applications 2022
Hauptverfasser: Bernardi, Olga, Florio, Anna, Wiseman, Jim
Format: Artikel
Sprache:eng
Schlagworte:
Dynamical Systems
Mathematics
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Zusammenfassung: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.
ISSN:0166-8641