Generalized dichotomies via time rescaling
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917453453328384 |
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| author | Dragicevic, Davor Silva, Cesar M. |
| author_facet | Dragicevic, Davor Silva, Cesar M. |
| contents | For discrete-time nonautonomous linear dynamics and a large class of discrete growth rates $μ$, we show that the notion of $μ$ dichotomy (with respect to a sequence of norms) can be completely characterized in terms of ordinary and exponential dichotomy (with respect to a sequence of norms) by employing a suitable rescaling of time. Previously, such a result was known only in the particular case of polynomial dichotomies. As a nontrivial application of our results, we study the structure of a generalized Sacker-Sell spectrum and obtain a series of nonautonomous topological and smooth linearization results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06630 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized dichotomies via time rescaling Dragicevic, Davor Silva, Cesar M. Dynamical Systems Classical Analysis and ODEs For discrete-time nonautonomous linear dynamics and a large class of discrete growth rates $μ$, we show that the notion of $μ$ dichotomy (with respect to a sequence of norms) can be completely characterized in terms of ordinary and exponential dichotomy (with respect to a sequence of norms) by employing a suitable rescaling of time. Previously, such a result was known only in the particular case of polynomial dichotomies. As a nontrivial application of our results, we study the structure of a generalized Sacker-Sell spectrum and obtain a series of nonautonomous topological and smooth linearization results. |
| title | Generalized dichotomies via time rescaling |
| topic | Dynamical Systems Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2501.06630 |