Morse Theory of Attractors via Lyapunov Functions
Dynamical Systems
2010-03-02 v1
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.
Cite
@article{arxiv.1003.0305,
title = {Morse Theory of Attractors via Lyapunov Functions},
author = {Desheng Li},
journal= {arXiv preprint arXiv:1003.0305},
year = {2010}
}