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

2020/11/19 by Bernardi, Olga, Florio, Anna, Wiseman, Jim
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.09830

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 SCR_d(ϕ). Such a result generalizes Conley's Fundamental Theorem of Dynamical Systems for the strong chain recurrent set.

Related

• Existence of Lipschitz continuous Lyapunov functions strict outside the\n strong chain recurrent set
• Notes on Chain Recurrence and Lyapunonv Functions
• Random Chain Recurrent Sets for Random Dynamical Systems
• The Fundamental Theorem of Dynamical Systems: all at once and all in the same place
• Lyapunov 1-forms for flows