Differentiable invariant manifolds of nilpotent parabolic points
| Autor: | Clara Cufí-Cabré, Ernest Fontich |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Varietats diferenciables Diagonalizable matrix Invariant manifold Dynamical Systems (math.DS) Type (model theory) Fixed point 01 natural sciences FOS: Mathematics Discrete Mathematics and Combinatorics Differentiable dynamical systems Differentiable function Mathematics - Dynamical Systems 0101 mathematics Differential (infinitesimal) Invariant (mathematics) Mathematics Differentiable manifolds Computer Science::Information Retrieval Applied Mathematics Primary: 37D10 Secondary: 37C25 Sistemes dinàmics diferenciables 010101 applied mathematics Nilpotent Parabolic point Parameterization method Analysis |
| Zdroj: | Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona Dipòsit Digital de la UB Universidad de Barcelona |
| Popis: | We consider a map $F$ of class $C^r$ 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 $C^r$ 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. Comment: 43 pages |
| Databáze: | OpenAIRE |
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