Partial section II: classification for general flows
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911304145436672 |
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| author | Marty, Théo |
| author_facet | Marty, Théo |
| contents | This is the second article in a series that aims at classifying partial sections of flows, that is a general family of transverse surfaces. In this part, we classify partial cross-sections for all continuous flows, in the spirit of Schwartzman-Fried-Sullivan theory.
We give a dynamical criterion for the existence of partial cross-sections, which is a direct consequence of part I of the series. Then we describe all partial cross-sections using a cohomological criterion, resembling Fried's criterion. We also characterize the cardinality of the set of partial cross-sections in a given cohomology class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05504 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partial section II: classification for general flows Marty, Théo Dynamical Systems 37C10 (Primary) 37B20 (Secondary) This is the second article in a series that aims at classifying partial sections of flows, that is a general family of transverse surfaces. In this part, we classify partial cross-sections for all continuous flows, in the spirit of Schwartzman-Fried-Sullivan theory. We give a dynamical criterion for the existence of partial cross-sections, which is a direct consequence of part I of the series. Then we describe all partial cross-sections using a cohomological criterion, resembling Fried's criterion. We also characterize the cardinality of the set of partial cross-sections in a given cohomology class. |
| title | Partial section II: classification for general flows |
| topic | Dynamical Systems 37C10 (Primary) 37B20 (Secondary) |
| url | https://arxiv.org/abs/2512.05504 |