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

Olga Bernardi , Anna Florio (1, 2) , Jim Wiseman (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Université Paris Dauphine-PSL
3 Agnes Scott College

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.

Domaines: Systèmes dynamiques [math.DS]

Olga Bernardi, Anna Florio, Jim Wiseman. A Conley-type Lyapunov function for the strong chain recurrent set. Topology and its Applications, 2022. ⟨hal-03847089⟩