Genericity of ergodicity for Sobolev homeomorphisms
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910920293220352 |
|---|---|
| author | Azevedo, Assis Azevedo, Davide Bessa, Mário Torres, Maria Joana |
| author_facet | Azevedo, Assis Azevedo, Davide Bessa, Mário Torres, Maria Joana |
| contents | In this paper we obtain a weak version of Lusin's theorem in the Sobolev-$(1,p)$ uniform closure of volume preserving Lipschitz homeomorphisms on closed and connected $d$-dimensional manifolds, $d \geq 2$ and $0<p<1$. With this result at hand we will be able to prove that the ergodic elements are generic. This establishes a version of Oxtoby and Ulam theorem for this Sobolev class. We also prove that, for $1\leq p<d-1$, the topological transitive maps are generic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18993 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Genericity of ergodicity for Sobolev homeomorphisms Azevedo, Assis Azevedo, Davide Bessa, Mário Torres, Maria Joana Dynamical Systems 37A25, 37A05, 46E36 (Primary) 37A60, 37B02, 37C20 (Secondary) In this paper we obtain a weak version of Lusin's theorem in the Sobolev-$(1,p)$ uniform closure of volume preserving Lipschitz homeomorphisms on closed and connected $d$-dimensional manifolds, $d \geq 2$ and $0<p<1$. With this result at hand we will be able to prove that the ergodic elements are generic. This establishes a version of Oxtoby and Ulam theorem for this Sobolev class. We also prove that, for $1\leq p<d-1$, the topological transitive maps are generic. |
| title | Genericity of ergodicity for Sobolev homeomorphisms |
| topic | Dynamical Systems 37A25, 37A05, 46E36 (Primary) 37A60, 37B02, 37C20 (Secondary) |
| url | https://arxiv.org/abs/2504.18993 |