No $C^1$-recurrence of iterations of symplectomorphisms
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912160431472640 |
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| author | Sugimoto, Yoshihiro |
| author_facet | Sugimoto, Yoshihiro |
| contents | In this article, we study the behavior of iterations of symplectomorphisms and Hamiltonian diffeomorphisms on symplectic manifolds. We prove that symplectomorphisms and Hamiltonian diffeomorphisms do not have $C^1$-recurrence on negatively monotone symplectic manifolds. This is a generalization of the results of the study of Polterovich, Ono, Atallah-Shelukhin. Hamiltonian group actions play very important roles in symplectic geometry. We see that negatively monotone symplectic manifolds are far from being Hamiltonian $G$-manifolds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_17917 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | No $C^1$-recurrence of iterations of symplectomorphisms Sugimoto, Yoshihiro Symplectic Geometry 53D05, 37J11 In this article, we study the behavior of iterations of symplectomorphisms and Hamiltonian diffeomorphisms on symplectic manifolds. We prove that symplectomorphisms and Hamiltonian diffeomorphisms do not have $C^1$-recurrence on negatively monotone symplectic manifolds. This is a generalization of the results of the study of Polterovich, Ono, Atallah-Shelukhin. Hamiltonian group actions play very important roles in symplectic geometry. We see that negatively monotone symplectic manifolds are far from being Hamiltonian $G$-manifolds. |
| title | No $C^1$-recurrence of iterations of symplectomorphisms |
| topic | Symplectic Geometry 53D05, 37J11 |
| url | https://arxiv.org/abs/2305.17917 |