Differentiable invariant manifolds of nilpotent parabolic points
We consider a map F of class Cr with a fixed point of parabolic type whose differential is not diagonalizable, and we study the existence and regularity of the invariant manifolds associated with the fixed point using the parameterization method. Concretely, we show that under suitable conditions on...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:257123 |
| Acesso em linha: | https://ddd.uab.cat/record/257123 https://dx.doi.org/urn:doi:10.3934/dcds.2021053 |
| Access Level: | acceso abierto |
| Palavra-chave: | Parabolic point Invariant manifold Parameterization method |
| Resumo: | We consider a map F of class Cr with a fixed point of parabolic type whose differential is not diagonalizable, and we study the existence and regularity of the invariant manifolds associated with the fixed point using the parameterization method. Concretely, we show that under suitable conditions on the coefficients of F, there exist invariant curves of class Cr away from the fixed point, and that they are analytic when F is analytic. The differentiability result is obtained as an application of the fiber contraction theorem. We also provide an algorithm to compute an approximation of a parameterization of the invariant curves and a normal form of the restricted dynamics of F on them. |
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