Morse Theory of Attractors via Lyapunov Functions

2010/03/01 by Desheng Li, Li, Desheng
Engineering · Physics and Astronomy · #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Model Reduction and Neural Networks #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1003.0305

openalex publication_date 2010/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the Morse theory of attractors for semiflows on complete metric spaces. First, we construct global Morse-Lyapunov functions for Morse decompositions of attractors. Then we extend some well known deformation results in the critical-point theory to Morse-Lyapunov functions which are only continuous. Based on these works, we finally introduce the concept of critical groups for Morse sets and establish Morse inequalities and Morse equations for attractors.

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