Smoothness of linearization by mixing parameters of dichotomy, bounded growth and perturbation
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909465571229696 |
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| author | Castañeda, Álvaro Huerta, Ignacio Robledo, Gonzalo |
| author_facet | Castañeda, Álvaro Huerta, Ignacio Robledo, Gonzalo |
| contents | We study the smoothness properties of a global and nonautonomous topological conjugacy between a linear system and a quasilinear perturbation. The linear system exhibits a nonuniform exponential dichotomy with a nontrivial projector and nonuniform bounded growth property. Additionally, the quasilinear perturbation is dominated by an increasing exponential function. Emphasis is placed on employing a set of parameters to describe the conditions of dichotomy, bounded growth and quasilinear perturbations. Finally, we prove that modifying these conditions enables us to achieve a broader smoothness interval. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19197 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smoothness of linearization by mixing parameters of dichotomy, bounded growth and perturbation Castañeda, Álvaro Huerta, Ignacio Robledo, Gonzalo Dynamical Systems Classical Analysis and ODEs 34D09, 37C60, 37B25 We study the smoothness properties of a global and nonautonomous topological conjugacy between a linear system and a quasilinear perturbation. The linear system exhibits a nonuniform exponential dichotomy with a nontrivial projector and nonuniform bounded growth property. Additionally, the quasilinear perturbation is dominated by an increasing exponential function. Emphasis is placed on employing a set of parameters to describe the conditions of dichotomy, bounded growth and quasilinear perturbations. Finally, we prove that modifying these conditions enables us to achieve a broader smoothness interval. |
| title | Smoothness of linearization by mixing parameters of dichotomy, bounded growth and perturbation |
| topic | Dynamical Systems Classical Analysis and ODEs 34D09, 37C60, 37B25 |
| url | https://arxiv.org/abs/2409.19197 |