Morse Theory of Attractors via Lyapunov Functions

Desheng Li

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arXiv · 1003.0305

Morse Theory of Attractors via Lyapunov Functions

Desheng Li

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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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BibTeX RIS

Desheng Li. 2010-03-01. Morse Theory of Attractors via Lyapunov Functions. https://arxiv.org/abs/1003.0305

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