Generalized Fiber Contraction Mapping Principle
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912154054033408 |
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| author | Luna, Alexandro Yang, Weiran |
| author_facet | Luna, Alexandro Yang, Weiran |
| contents | We prove a generalized non-stationary version of the fiber contraction mapping theorem. It was originally used in [HirschPugh70] to prove that the stable foliation of a $C^2$ Anosov diffeomorphism of a surface is $C^1$. Our generalized principle is used in [Luna24], where an analogous regularity result for stable foliations of non-stationary systems is proved. The result is stated in a general setting so that it may be used in future dynamical results in the random and non-stationary settings, especially for graph transform arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09767 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Fiber Contraction Mapping Principle Luna, Alexandro Yang, Weiran Dynamical Systems We prove a generalized non-stationary version of the fiber contraction mapping theorem. It was originally used in [HirschPugh70] to prove that the stable foliation of a $C^2$ Anosov diffeomorphism of a surface is $C^1$. Our generalized principle is used in [Luna24], where an analogous regularity result for stable foliations of non-stationary systems is proved. The result is stated in a general setting so that it may be used in future dynamical results in the random and non-stationary settings, especially for graph transform arguments. |
| title | Generalized Fiber Contraction Mapping Principle |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2412.09767 |