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