The number of periodic points of surface symplectic diffeomorphisms
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913576285896704 |
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| author | Atallah, Marcelo S. Batoréo, Marta Ferreira, Brayan |
| author_facet | Atallah, Marcelo S. Batoréo, Marta Ferreira, Brayan |
| contents | We use symplectic tools to establish a smooth variant of Franks theorem for a closed orientable surface of positive genus $g$; it implies that a symplectic diffeomorphism isotopic to the identity with more than $2g-2$ fixed points, counted homologically, has infinitely many periodic points. Furthermore, we present examples of symplectic diffeomorphisms with a prescribed number of periodic points. In particular, we construct symplectic flows on surfaces possessing only one fixed point and no other periodic orbits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14962 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The number of periodic points of surface symplectic diffeomorphisms Atallah, Marcelo S. Batoréo, Marta Ferreira, Brayan Symplectic Geometry Dynamical Systems We use symplectic tools to establish a smooth variant of Franks theorem for a closed orientable surface of positive genus $g$; it implies that a symplectic diffeomorphism isotopic to the identity with more than $2g-2$ fixed points, counted homologically, has infinitely many periodic points. Furthermore, we present examples of symplectic diffeomorphisms with a prescribed number of periodic points. In particular, we construct symplectic flows on surfaces possessing only one fixed point and no other periodic orbits. |
| title | The number of periodic points of surface symplectic diffeomorphisms |
| topic | Symplectic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2409.14962 |