Normal forms in a neighborhood of hyperbolic periodic orbits for flows in dimension 3
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909950492540928 |
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| author | Erchenko, Alena Vinhage, Kurt Yang, Yun |
| author_facet | Erchenko, Alena Vinhage, Kurt Yang, Yun |
| contents | In a neighborhood of a hyperbolic periodic orbit of a volume-preserving flow on a manifold of dimension 3, we define and show the existence of a normal form for the generator of the flow that encodes the dynamics. If the flow is a contact flow, we show the existence of a normal form for the contact form what results in an improved normal form for its Reeb vector field. Additionally, we present a few rigidity results associated to periodic data for Anosov contact flows derived from the underlying normal form theory. Finally, we establish a new local rigidity result for contact flows on manifolds of dimension 3 in a neighborhood of a hyperbolic periodic point by finding a new link between the roof function and the return map to a section. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normal forms in a neighborhood of hyperbolic periodic orbits for flows in dimension 3 Erchenko, Alena Vinhage, Kurt Yang, Yun Dynamical Systems Symplectic Geometry In a neighborhood of a hyperbolic periodic orbit of a volume-preserving flow on a manifold of dimension 3, we define and show the existence of a normal form for the generator of the flow that encodes the dynamics. If the flow is a contact flow, we show the existence of a normal form for the contact form what results in an improved normal form for its Reeb vector field. Additionally, we present a few rigidity results associated to periodic data for Anosov contact flows derived from the underlying normal form theory. Finally, we establish a new local rigidity result for contact flows on manifolds of dimension 3 in a neighborhood of a hyperbolic periodic point by finding a new link between the roof function and the return map to a section. |
| title | Normal forms in a neighborhood of hyperbolic periodic orbits for flows in dimension 3 |
| topic | Dynamical Systems Symplectic Geometry |
| url | https://arxiv.org/abs/2512.08051 |