Global stability of discretized Anosov flows

IF 0.7 1区 数学 Q2 MATHEMATICS Journal of Modern Dynamics Pub Date : 2022-04-08 DOI:10.3934/jmd.2023016
Santiago Martinchich
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引用次数: 5

Abstract

The goal of this article is to establish several general properties of a somewhat large class of partially hyperbolic diffeomorphisms called \emph{discretized Anosov flows}. A general definition for these systems is presented and is proven to be equivalent with the definition introduced in [BFFP19], as well as with the notion of flow type partially hyperbolic diffeomorphisms introduced in [BFT20]. The set of discretized Anosov flows is shown to be $C^1$ open and closed inside the set of partially hyperbolic diffeomorphisms. Every discretized Anosov flow is proven to be dynamically coherent and plaque expansive. Unique integrability of the center bundle is shown to happen for whole connected components, notably the ones containing the time 1 map of an Anosov flow. For general connected components, a result on uniqueness of invariant foliation is obtained. Similar results are seen to happen for partially hyperbolic systems admitting a uniformly compact center foliation extending the studies initiated in [BB16].
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离散化Anosov流的全局稳定性
本文的目的是建立一个比较大的类部分双曲微分同态称为\emph{离散Anosov流}的几个一般性质。本文给出了这些系统的一般定义,并被证明与[BFFP19]中引入的定义以及[BFT20]中引入的流型部分双曲微分同态的概念是等价的。离散化的Anosov流集在部分双曲微分同态集内是$C^1$开闭的。每个离散的阿诺索夫流被证明是动态相干和斑块膨胀。中心束的唯一可积性被证明发生在整个连接的组件,特别是那些包含一个Anosov流的时间1映射。对于一般连通分量,得到了不变叶化唯一性的结果。类似的结果也出现在部分双曲系统中,其中心叶理均匀致密,扩展了[BB16]中开始的研究。
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
CiteScore
1.30
自引率
0.00%
发文量
11
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.
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