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...
| Autores: | , , , |
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| 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 |
| 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. |
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