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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.04994 |
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| _version_ | 1866909943715594240 |
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| author | Marty, Théo |
| author_facet | Marty, Théo |
| contents | This is the first article in a series that aims at classifying partial sections of flows, that is a general family of transverse surfaces. In this part, we deal with the dynamical aspect of the question.
Given a flow on a compact manifold $M$ and a cohomology class $α$ of rank 1, we give a criterion for the existence of an $α$-equivariant Lyapunov map on an Abelian covering of $M$ associated to $α$.
One important aspect of the existence of such Lyapunov maps, and of the classification of partial sections, is a type of recurrence set relative to $α$. We describe how that set depends on $α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04994 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partial section I: $α$-recurrence and equivariant Lyapunov maps Marty, Théo Dynamical Systems 37C10 (Primary) 37B20 (Secondary) This is the first article in a series that aims at classifying partial sections of flows, that is a general family of transverse surfaces. In this part, we deal with the dynamical aspect of the question. Given a flow on a compact manifold $M$ and a cohomology class $α$ of rank 1, we give a criterion for the existence of an $α$-equivariant Lyapunov map on an Abelian covering of $M$ associated to $α$. One important aspect of the existence of such Lyapunov maps, and of the classification of partial sections, is a type of recurrence set relative to $α$. We describe how that set depends on $α$. |
| title | Partial section I: $α$-recurrence and equivariant Lyapunov maps |
| topic | Dynamical Systems 37C10 (Primary) 37B20 (Secondary) |
| url | https://arxiv.org/abs/2512.04994 |