曲面上的非自治曲线

IF 0.7 1区数学 Q2 MATHEMATICS

Journal of Modern Dynamics Pub Date : 2019-06-19 DOI:10.3934/jmd.2021010

M. Khanevsky

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引用次数: 4

摘要

考虑具有两条适当嵌入的哈密顿同位素曲线$L$和$L'$的辛曲面$\Sigma$。假设Ham（\ Sigma）$中的$g\是一个哈密顿微分同胚，它将$L$发送到$L'$。$g$的哪些动力学性质可以被对$（L，L'）$检测到？我们讨论了两种情况，其中可以推断$g$是“混沌”的：非自治的，甚至是正熵的。

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Non-autonomous curves on surfaces

Consider a symplectic surface $\Sigma$ with two properly embedded Hamiltonian isotopic curves $L$ and $L'$. Suppose $g \in Ham (\Sigma)$ is a Hamiltonian diffeomorphism which sends $L$ to $L'$. Which dynamical properties of $g$ can be detected by the pair $(L, L')$? We discuss two cases where one can deduce that $g$ is `chaotic': non-autonomous or even of positive entropy.

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来源期刊

Journal of Modern Dynamics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Modern Dynamics (JMD) is dedicated to publishing research articles in active and promising areas in the theory of dynamical systems with particular emphasis on the mutual interaction between dynamics and other major areas of mathematical research, including: Number theory Symplectic geometry Differential geometry Rigidity Quantum chaos Teichmüller theory Geometric group theory Harmonic analysis on manifolds. The journal is published by the American Institute of Mathematical Sciences (AIMS) with the support of the Anatole Katok Center for Dynamical Systems and Geometry at the Pennsylvania State University.