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arXiv · 2305.17917

No $C^1$-recurrence of iterations of symplectomorphisms

Yoshihiro Sugimoto
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Abstract

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.

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Yoshihiro Sugimoto. 2023-05-29. No $C^1$-recurrence of iterations of symplectomorphisms. https://doi.org/10.1007/s10711-024-00969-1

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