Katok的马蹄铁定理在保守的C^2曲面微分同态中的一个有效版本

IF 0.7 1区数学 Q2 MATHEMATICS

Journal of Modern Dynamics Pub Date : 2017-03-18 DOI:10.3934/JMD.2017017

B. Fayad, Zhiyuan Zhang

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引用次数: 2

摘要

对于保面积的C2曲面微分同胚，我们给出了一个关于覆盖正比例空间所需的Bowen（n，δ）-球数的指数增长的显式有限信息条件，该条件足以保证正拓扑熵。这可以被视为在保守环境中卡托克马蹄定理的一个有效版本。我们还证明了类似的结果在大于3的维度上是错误的。

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An effective version of Katok's horseshoe theorem for conservative $C^2$ surface diffeomorphisms

For area preserving C2 surface diffeomorphisms, we give an explicit finite information condition on the exponential growth of the number of Bowen's (n, δ)-balls needed to cover a positive proportion of the space, that is sufficient to guarantee positive topological entropy. This can be seen as an effective version of Katok's horseshoe theorem in the conservative setting. We also show that the analogous result is false in dimension larger than 3.

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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.