论文标题
在表面上可集成和自主哈密顿的差异性之间的HOFER度量的差距
A gap in the Hofer metric between integrable and autonomous Hamiltonian diffeomorphisms on surfaces
论文作者
论文摘要
令$σ$为配备区域形式的紧凑型表面。 There is an long standing open question by Katok, which, in particular, asks whether every entropy-zero Hamiltonian diffeomorphism of a surface lies in the $C^0$-closure of the set of integrable diffeomorphisms.这个问题的自然概括是询问一个“简单”的哈密顿量差异$σ$的差异性在多大程度上可以由对方近似。在本文中，我们表明，在一组可综合的哈密顿人中，一组自主哈密顿的差异性并不是Hofer浓度。我们构建了可集成的差异性的明确示例，这些示例不能被自主构建。
Let $Σ$ be a compact surface equipped with an area form. There is an long standing open question by Katok, which, in particular, asks whether every entropy-zero Hamiltonian diffeomorphism of a surface lies in the $C^0$-closure of the set of integrable diffeomorphisms. A natural generalization of this question is to ask to what extent one family of `simple' Hamiltonian diffeomorphisms of $Σ$ can be approximated by the other. In this paper we show that the set of autonomous Hamiltonian diffeomorphisms is not Hofer-dense in the set of integrable Hamiltonians. We construct explicit examples of integrable diffeomorphisms which cannot be Hofer-approximated by autonomous ones.
