Morse decomposition of global attractors with infinite components

In this paper we describe some dynamical properties of a Morse decomposition with a countable number of sets. In particular, we are able to prove that the gradient dynamics on Morse sets together with a separation assumption is equivalent to the existence of an ordered Lyapunov function associated t...

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Detalles Bibliográficos
Autores: Caraballo Garrido, Tomás, Jara Pérez, Juan Carlos, Langa Rosado, José Antonio, Valero Cuadra, José
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/29021
Acceso en línea:http://hdl.handle.net/11441/29021
https://doi.org/10.3934/dcds.2015.35.2845
Access Level:acceso abierto
Palabra clave:Morse decomposition
infinite components
gradient dynamics
Lyapunov function
gradient-like semigroup
Descripción
Sumario:In this paper we describe some dynamical properties of a Morse decomposition with a countable number of sets. In particular, we are able to prove that the gradient dynamics on Morse sets together with a separation assumption is equivalent to the existence of an ordered Lyapunov function associated to the Morse sets and also to the existence of a Morse decomposition -that is, the global attractor can be described as an increasing family of local attractors and their associated repellers.