Smooth Morse-Lyapunov Functions and Morse Theory of Strong Attractors for Nonsmooth Dynamical Systems

Details Smooth Morse-Lyapunov Functions and Morse Theory of Strong Attractors for Nonsmooth Dynamical Systems Smooth Morse-Lyapunov Functions and Morse Theory of Strong Attractors for Nonsmooth Dynamical Systems

2010-01-11

arxiv.org/abs/1001.1576v2

Mathematics

Dynamical Systems

36 pages

Scientific paper

In this paper we first construct smooth Morse-Lyapunov functions of
attractors for nonsmooth dynamical systems. Then we prove that all open
attractor neighborhoods of an attractor have the same homotopy type. Based on
this basic fact we finally introduce the concept of critical group for Morse
sets of an attractor and establish Morse inequalities and equations.

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