Gradient Infinite-Dimensional Random Dynamical Systems
In this paper we introduce the concept of a gradient random dynamical system as a random semiflow possessing a continuous random Lyapunov function which describes the asymptotic regime of the system. Thus, we are able to analyze the dynamical properties on a random attractor described by its Morse d...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/23674 |
| Acceso en línea: | http://hdl.handle.net/11441/23674 https://doi.org/10.1137/120862752 |
| Access Level: | acceso abierto |
| Palabra clave: | Morse decomposition attractor repeller Morse set Lyapunov function random dynamical systems |
| Sumario: | In this paper we introduce the concept of a gradient random dynamical system as a random semiflow possessing a continuous random Lyapunov function which describes the asymptotic regime of the system. Thus, we are able to analyze the dynamical properties on a random attractor described by its Morse decomposition for infinite-dimensional random dynamical systems. In particular, if a random attractor is characterized by a family of invariant random compact sets, we show the equivalence among the asymptotic stability of this family, the Morse decomposition of the random attractor, and the existence of a random Lyapunov function. |
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