Symbolic dynamics for pointwise hyperbolic systems on open regions

IF 0.8 3区数学 Q2 MATHEMATICS

Ergodic Theory and Dynamical Systems Pub Date : 2024-09-10 DOI:10.1017/etds.2024.47

CHUPENG WU, YUNHUA ZHOU

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引用次数: 0

Abstract

Under certain conditions, we construct a countable Markov partition for pointwise hyperbolic diffeomorphism

$f:M\rightarrow M$

on an open invariant subset

$O\subset M$

, which allows the Lyapunov exponents to be zero. From this partition, we define a symbolic extension that is finite-to-one and onto a subset of O that carries the same finite f-invariant measures as O. Our method relies upon shadowing theory of a recurrent-pointwise-pseudo-orbit that we introduce. As a canonical application, we estimate the number of closed orbits for f.

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开放区域上点双曲系统的符号动力学

在某些条件下，我们在开放不变子集 $O\subset M$ 上为点式双曲衍射 $f:M\rightarrow M$ 构造了一个可数马尔可夫分区，它允许 Lyapunov 指数为零。从这个分区出发，我们定义了一个符号扩展，它是有限对一的，并扩展到 O 的一个子集上，该子集携带与 O 相同的有限 f 不变度量。作为一个典型应用，我们估算了 f 的闭合轨道数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Ergodic Theory and Dynamical Systems 数学-数学

CiteScore

1.70

自引率

11.10%

发文量

113

审稿时长

6-12 weeks

期刊介绍： Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ as common themes global dynamical methods. The journal provides a focus for this important and flourishing area of mathematics and brings together many major contributions in the field. The journal acts as a forum for central problems of dynamical systems and of interactions of dynamical systems with areas such as differential geometry, number theory, operator algebras, celestial and statistical mechanics, and biology.