Morse Decompositions with Infinite Components for Multivalued Semiflows |
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| Authors: | Henrique B da Costa José Valero |
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| Institution: | 1.Instituto de Ciências Matemáticas e de Computa??o (ICMC),Universidade de S?o Paulo (USP),S?o Carlos,Brazil;2.Centro de Investigación Operativa,Universidad Miguel Hernández de Elche,Elche,Spain |
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| Abstract: | 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.This theorem is applied to a reaction-diffusion inclusion with an infinite number of equilibria. |
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