Anti-classification for flows on two-tori
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913827873882112 |
|---|---|
| author | Goncharuk, Nataliya |
| author_facet | Goncharuk, Nataliya |
| contents | We prove that the classification of real-analytic vector fields on the two-torus up to orbital topological equivalence does not admit a complete numerical invariant that is a Borel function. Moreover, smooth vector fields that are difficult to classify appear in generic smooth 7-parameter families. In dimension 2, this improves the recent result of Gorodetski and Foreman (arXiv:2206.09322) for non-classifiability of smooth diffeomorphisms up to continuous conjugacy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18847 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anti-classification for flows on two-tori Goncharuk, Nataliya Dynamical Systems Logic 37E35, 54H05, 03E15 We prove that the classification of real-analytic vector fields on the two-torus up to orbital topological equivalence does not admit a complete numerical invariant that is a Borel function. Moreover, smooth vector fields that are difficult to classify appear in generic smooth 7-parameter families. In dimension 2, this improves the recent result of Gorodetski and Foreman (arXiv:2206.09322) for non-classifiability of smooth diffeomorphisms up to continuous conjugacy. |
| title | Anti-classification for flows on two-tori |
| topic | Dynamical Systems Logic 37E35, 54H05, 03E15 |
| url | https://arxiv.org/abs/2503.18847 |