All, most, some? On diffeomorphisms of the interval that are distorted and/or conjugate to powers of themselves
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913356681576448 |
|---|---|
| author | Eynard-Bontemps, Hélène Navas, Andrés |
| author_facet | Eynard-Bontemps, Hélène Navas, Andrés |
| contents | We study the problem of conjugating a diffeomorphism of the interval to (positive) powers of itself. Although this is always possible for homeomorphisms, the smooth setting is rather interesting. Besides the obvious obstruction given by hyperbolic fixed points, several other aspects need to be considered. As concrete results we show that, in class $C^1$, if we restrict to the (closed) subset of diffeomorphisms having only parabolic fixed points, then the set of diffeomorphisms that are conjugate to their powers is dense, but its complement is generic. In higher regularity, however, the complementary set contains an open and dense set. The text is complemented with several remarks and results concerning distortion elements of the group of diffeomorphisms of the interval in several regularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11366 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | All, most, some? On diffeomorphisms of the interval that are distorted and/or conjugate to powers of themselves Eynard-Bontemps, Hélène Navas, Andrés Dynamical Systems 37C05, 37C10, 37C15, 37C85, 37E05, 57M60. 37C05, 37C10, 37C15, 37C85, 37E05, 57M60. 37C05, 37C10, 37C15, 37C85, 37E05, 37M60 We study the problem of conjugating a diffeomorphism of the interval to (positive) powers of itself. Although this is always possible for homeomorphisms, the smooth setting is rather interesting. Besides the obvious obstruction given by hyperbolic fixed points, several other aspects need to be considered. As concrete results we show that, in class $C^1$, if we restrict to the (closed) subset of diffeomorphisms having only parabolic fixed points, then the set of diffeomorphisms that are conjugate to their powers is dense, but its complement is generic. In higher regularity, however, the complementary set contains an open and dense set. The text is complemented with several remarks and results concerning distortion elements of the group of diffeomorphisms of the interval in several regularities. |
| title | All, most, some? On diffeomorphisms of the interval that are distorted and/or conjugate to powers of themselves |
| topic | Dynamical Systems 37C05, 37C10, 37C15, 37C85, 37E05, 57M60. 37C05, 37C10, 37C15, 37C85, 37E05, 57M60. 37C05, 37C10, 37C15, 37C85, 37E05, 37M60 |
| url | https://arxiv.org/abs/2405.11366 |