论动作与衔接的关系

IF 0.7 1区数学 Q2 MATHEMATICS

Journal of Modern Dynamics Pub Date : 2020-06-11 DOI:10.3934/jmd.2021011

David Bechara Senior, Umberto L. Hryniewicz, Pedro A. S. Salomão

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引用次数: 7

摘要

我们引入了三维接触形式的数值不变量，并使用渐近循环来估计它们。因此，我们证明了Hutchings和Weiler关于周期点平均作用的结果的Anosov-Reeb流的一个版本。主要工具是动作链接引理，将由周期轨道界定的表面的接触面积表示为大多数轨迹与表面的渐近相交数的刘维尔平均值。

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On the relation between action and linking

We introduce numerical invariants of contact forms in dimension three and use asymptotic cycles to estimate them. As a consequence, we prove a version for Anosov Reeb flows of results due to Hutchings and Weiler on mean actions of periodic points. The main tool is the Action-Linking Lemma, expressing the contact area of a surface bounded by periodic orbits as the Liouville average of the asymptotic intersection number of most trajectories with the surface.

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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.