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math.DS2010★ 6 cited
Morse Theory of Attractors via Lyapunov Functions
Desheng Li
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…
math.DS2010
Smooth Morse-Lyapunov Functions and Morse Theory of Strong Attractors for Nonsmooth Dynamical Systems
Desheng Li
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…