Effective SPR property for surface diffeomorphisms and three-dimensional vector fields
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909941761048576 |
|---|---|
| author | Burguet, David Luo, Chiyi Yang, Dawei |
| author_facet | Burguet, David Luo, Chiyi Yang, Dawei |
| contents | In this paper, we prove that ergodic measures with large entropy give uniformly large measure to the set of points with simultaneously long unstable and long stable manifolds. As a consequence, for $C^{\infty}$ surface diffeomorphisms, we establish an effective version of the SPR property. For $C^{\infty}$ three-dimensional flows without singularities, we prove the finiteness of equilibrium measures for admissible potentials whose variation is strictly less than half of the topological entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03515 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effective SPR property for surface diffeomorphisms and three-dimensional vector fields Burguet, David Luo, Chiyi Yang, Dawei Dynamical Systems In this paper, we prove that ergodic measures with large entropy give uniformly large measure to the set of points with simultaneously long unstable and long stable manifolds. As a consequence, for $C^{\infty}$ surface diffeomorphisms, we establish an effective version of the SPR property. For $C^{\infty}$ three-dimensional flows without singularities, we prove the finiteness of equilibrium measures for admissible potentials whose variation is strictly less than half of the topological entropy. |
| title | Effective SPR property for surface diffeomorphisms and three-dimensional vector fields |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2512.03515 |