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A Conley-type Lyapunov function for the strong chain recurrent set
Topology and its Applications ( IF 0.6 ) Pub Date : 2021-07-07 , DOI: 10.1016/j.topol.2021.107768
Olga Bernardi 1 , Anna Florio 2 , Jim Wiseman 3
Affiliation  

Let ϕ:X×RX be a continuous flow on a compact metric space (X,d). In this article we constructively prove the existence of a continuous Lyapunov function for ϕ which is strictly decreasing outside SCRd(ϕ). Such a result generalizes Conley's Fundamental Theorem of Dynamical Systems for the strong chain recurrent set.



中文翻译:

强链循环集的Conley型Lyapunov函数

φX×电阻X 是紧致度量空间上的连续流 (X,d). 在本文中,我们建设性地证明了ϕ的连续李雅普诺夫函数的存在性,该函数在外部严格递减可控硅d(φ). 这样的结果概括了强链循环集的康利动力系统基本定理。

更新日期:2021-07-07
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