Fixed point theorems for small divisors problems
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915999333220352 |
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| author | Garay, Mauricio van Straten, Duco |
| author_facet | Garay, Mauricio van Straten, Duco |
| contents | In the seventies', Zehnder found a Nash-Moser type implicit function theorem in the analytic set-up. This theorem has found many applications in dynamical systems although its applications require, as a general rule, some efforts. We develop further the analytic theory and give fixed point theorems with direct applications to the study of dynamical systems.In practice, our theorems show that Bruno conditions are sufficient to ensure the existence of a positive measure set of invariant tori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19808 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed point theorems for small divisors problems Garay, Mauricio van Straten, Duco Dynamical Systems Functional Analysis 47J07 In the seventies', Zehnder found a Nash-Moser type implicit function theorem in the analytic set-up. This theorem has found many applications in dynamical systems although its applications require, as a general rule, some efforts. We develop further the analytic theory and give fixed point theorems with direct applications to the study of dynamical systems.In practice, our theorems show that Bruno conditions are sufficient to ensure the existence of a positive measure set of invariant tori. |
| title | Fixed point theorems for small divisors problems |
| topic | Dynamical Systems Functional Analysis 47J07 |
| url | https://arxiv.org/abs/2504.19808 |