Takens Theorem for nonautonomous partially hyperbolic dynamical systems
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912038479986688 |
|---|---|
| author | Dragičević, Davor Tang, Xiao Zhang, Wenmeng |
| author_facet | Dragičević, Davor Tang, Xiao Zhang, Wenmeng |
| contents | Takens Theorem for a partially hyperbolic dynamics provides a normal linearization along the center manifold. In this paper, we give the nonautonomous version of Takens Theorem under non-resonance conditions formulated in terms of the dichotomy spectrum. In our proof, one difficulty is to solve homological equations for the normal form theory which involve a center variable, while another difficulty is to find the dichotomy spectrum of a certain matrix cocycle that is block lower triangular. In order to overcome those difficulties, in comparison with the autonomous case, we need an additional term in the (nonautonomous) non-resonance conditions to guarantee certain spectral gap conditions. This additional term disappears naturally in the autonomous case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10535 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Takens Theorem for nonautonomous partially hyperbolic dynamical systems Dragičević, Davor Tang, Xiao Zhang, Wenmeng Dynamical Systems Classical Analysis and ODEs Takens Theorem for a partially hyperbolic dynamics provides a normal linearization along the center manifold. In this paper, we give the nonautonomous version of Takens Theorem under non-resonance conditions formulated in terms of the dichotomy spectrum. In our proof, one difficulty is to solve homological equations for the normal form theory which involve a center variable, while another difficulty is to find the dichotomy spectrum of a certain matrix cocycle that is block lower triangular. In order to overcome those difficulties, in comparison with the autonomous case, we need an additional term in the (nonautonomous) non-resonance conditions to guarantee certain spectral gap conditions. This additional term disappears naturally in the autonomous case. |
| title | Takens Theorem for nonautonomous partially hyperbolic dynamical systems |
| topic | Dynamical Systems Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2310.10535 |