Symmetric periodic Reeb orbits on the sphere
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866914767284731904 |
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| author | Abreu, Miguel Liu, Hui Macarini, Leonardo |
| author_facet | Abreu, Miguel Liu, Hui Macarini, Leonardo |
| contents | A long standing conjecture in Hamiltonian Dynamics states that every contact form on the standard contact sphere $S^{2n+1}$ has at least $n+1$ simple periodic Reeb orbits. In this work, we consider a refinement of this problem when the contact form has a suitable symmetry and we ask if there are at least $n+1$ simple symmetric periodic orbits. We show that there is at least one symmetric periodic orbit for any contact form and at least two symmetric closed orbits whenever the contact form is dynamically convex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_16470 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Symmetric periodic Reeb orbits on the sphere Abreu, Miguel Liu, Hui Macarini, Leonardo Symplectic Geometry Dynamical Systems 53D40, 37J10, 37J55 A long standing conjecture in Hamiltonian Dynamics states that every contact form on the standard contact sphere $S^{2n+1}$ has at least $n+1$ simple periodic Reeb orbits. In this work, we consider a refinement of this problem when the contact form has a suitable symmetry and we ask if there are at least $n+1$ simple symmetric periodic orbits. We show that there is at least one symmetric periodic orbit for any contact form and at least two symmetric closed orbits whenever the contact form is dynamically convex. |
| title | Symmetric periodic Reeb orbits on the sphere |
| topic | Symplectic Geometry Dynamical Systems 53D40, 37J10, 37J55 |
| url | https://arxiv.org/abs/2211.16470 |