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http://hdl.handle.net/2445/183479
Title: | Differentiable invariant manifolds of nilpotent parabolic points |
Author: | Cufí Cabré, Clara Fontich, Ernest, 1955- |
Keywords: | Sistemes dinàmics diferenciables Varietats diferenciables Differentiable dynamical systems Differentiable manifolds |
Issue Date: | Oct-2021 |
Publisher: | American Institute of Mathematical Sciences (AIMS) |
Abstract: | 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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.3934/dcds.2021053 |
It is part of: | Discrete and Continuous Dynamical Systems-Series A, 2021, vol. 41, num. 10, p. 4667- 4704 |
URI: | http://hdl.handle.net/2445/183479 |
Related resource: | https://doi.org/10.3934/dcds.2021053 |
ISSN: | 1078-0947 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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720158.pdf | 237.84 kB | Adobe PDF | View/Open |
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