The parameterization method for invariant manifolds III: overview and applications
We describe a method to establish existence and regularity of invariant manifolds and, at the same time to find simple maps which are conjugated to the dynamics on them. The method establishes several invariant manifold theorems. For instance, it reduces the proof of the usual stable manifold theore...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2003 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/910 |
| Acesso em linha: | https://hdl.handle.net/2117/910 |
| Access Level: | acceso abierto |
| Palavra-chave: | Differentiable dynamical systems invariant manifolds Sistemes dinàmics diferenciables Teoria ergòdica Classificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behavior Classificació AMS::37 Dynamical systems and ergodic theory::37M Approximation methods and numerical treatment of dynamical systems |
| Resumo: | We describe a method to establish existence and regularity of invariant manifolds and, at the same time to find simple maps which are conjugated to the dynamics on them. The method establishes several invariant manifold theorems. For instance, it reduces the proof of the usual stable manifold theorem near hyperbolic points to an application of the implicit function theorem in Banach spaces. We also present several other applications of the method. |
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