Title: Non contractible periodic orbits for generic hamiltonian diffeomorphisms of surfaces Show Chinese title

Title: 不可缩的周期轨道对于曲面的通用哈密顿微分同胚

Abstract: Let $S$ be a closed surface of genus $g\geq 1$, furnished with an area form $\omega$. We show that there exists an open and dense set ${\mathcal O_r}$ of the space of Hamiltonian diffeomorphisms of class $C^r$, $1\leq r\leq\infty$, endowed with the $C^r$-topology, such that every $f\in \mathcal O_r$ possesses infinitely many non contractible periodic orbits. We obtain a positive answer to a question asked by Viktor Ginzburg and Ba\c{s}ak G\"{u}rel. The proof is a consequence of recent previous works of the authors [LecSa]. Show Chinese abstract

Abstract: 设$S$为一个亏格为$g\geq 1$的闭曲面，配备有面积形式$\omega$。 我们证明在具有$C^r$-拓扑的类$C^r$,$1\leq r\leq\infty$的哈密顿微分同胚空间中存在一个开且稠密的集合${\mathcal O_r}$，使得每个$f\in \mathcal O_r$都具有无限多个不可收缩的周期轨道。 我们得到了维克多·金茨堡和巴沙克·居雷尔提出的问题的肯定回答。 证明是作者之前最近工作的结果 [LecSa]。