Morse Decompositions with Infinite Components for Multivalued Semiflows

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• 作者：Henrique B. da Costa ; José Valero
• 关键词：Set ; valued dynamical systems ; Morse decomposition ; Gradient dynamics ; Lyapunov function
• 刊名：Set-Valued and Variational Analysis
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：25
• 期：1
• 页码：25-41
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Probability Theory and Stochastic Processes;
• 出版者：Springer Netherlands
• ISSN：1877-0541
• 卷排序：25

文摘

In this paper we study the theory of Morse decompositions with an infinite number of components in the multivalued framework, proving that for a disjoint infinite family of weakly invariant sets (being all isolated but one) a Lyapunov function ordering them exists if and only if the multivalued semiflow is dynamically gradient. Moreover, these properties are equivalent to the existence of a Morse decomposition.