A $C^\infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces
A $C^\infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces
复制标题
闭曲面哈密顿微分同胚的 $C^infty$ 闭引理
DOI：
10.1007/s00039-016-0386-3
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发表时间：
2016
影响因子：
2.2
通讯作者：
Kei Irie
中科院分区：
文献类型：
--
作者：
Masayuki Asaoka;Kei Irie
本文证明了闭曲面的Hamilton同态的闭引理。这是闭切触三流形上Reeb流的封闭引理的结果，最近被证明是谱不变量在嵌入切触同调中的应用。本文的一个关键的新成分是分析的面积保持映射附近的不动点，这是基于一些经典的结果在哈密顿动力学：存在KAM不变圆椭圆不动点，和双曲不动点的Birkhoff规范形的收敛性。
We prove aclosing lemma for Hamiltonian diffeomorphisms of closed surfaces. This is a consequence of aclosing lemma for Reeb flows on closed contact three-manifolds, which was recently proved as an application of spectral invariants in embedded contact homology. A key new ingredient of this paper is an analysis of an area-preserving map near its fixed point, which is based on some classical results in Hamiltonian dynamics: existence of KAM invariant circles for elliptic fixed points, and convergence of the Birkhoff normal form for hyperbolic fixed points.