On residues and conjugacies for germs of 1-D parabolic diffeomorphisms in finite regularity
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912247902633984 |
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| author | Eynard-Bontemps, Hélène Navas, Andrés |
| author_facet | Eynard-Bontemps, Hélène Navas, Andrés |
| contents | We study conjugacy classes of germs of non-flat diffeomorphisms of the real line fixing the origin. Based on the work of Takens and Yoccoz, we establish results that are sharp in terms of differentiability classes and order of tangency to the identity. The core of all of this lies in the invariance of residues under low-regular conjugacies. This may be seen as an extension of the fact (also proved in this article) that the value of the Schwarzian derivative at the origin for germs of $C^3$ parabolic diffeomorphisms is invariant under $C^2$ parabolic conjugacy, though it may vary arbitrarily under parabolic $C^1$ conjugacy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_13182 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On residues and conjugacies for germs of 1-D parabolic diffeomorphisms in finite regularity Eynard-Bontemps, Hélène Navas, Andrés Dynamical Systems Analysis of PDEs Group Theory Geometric Topology 20F38, 37C25, 37E99 We study conjugacy classes of germs of non-flat diffeomorphisms of the real line fixing the origin. Based on the work of Takens and Yoccoz, we establish results that are sharp in terms of differentiability classes and order of tangency to the identity. The core of all of this lies in the invariance of residues under low-regular conjugacies. This may be seen as an extension of the fact (also proved in this article) that the value of the Schwarzian derivative at the origin for germs of $C^3$ parabolic diffeomorphisms is invariant under $C^2$ parabolic conjugacy, though it may vary arbitrarily under parabolic $C^1$ conjugacy. |
| title | On residues and conjugacies for germs of 1-D parabolic diffeomorphisms in finite regularity |
| topic | Dynamical Systems Analysis of PDEs Group Theory Geometric Topology 20F38, 37C25, 37E99 |
| url | https://arxiv.org/abs/2302.13182 |