余维数为1的部分双曲微分同态

IF 1.1 3区数学 Q1 MATHEMATICS

Discrete and Continuous Dynamical Systems Pub Date : 2022-11-02 DOI:10.3934/dcds.2023066

Xiang Zhang

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引用次数: 0

摘要

我们证明了在$\mathbb{T}^{n}$上必须支持每一个余维数为1的部分双曲微分同态。它是局部唯一可积的，由一个线性余维的Anosov微分同态导出。此外，该系统本质上是遍历的，并且A. Katok关于具有中间熵的遍历测度的存在性的猜想也成立。

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On codimension one partially hyperbolic diffeomorphisms

We show that every codimension one partially hyperbolic diffeomorphism must support on $\mathbb{T}^{n}$. It is locally uniquely integrable and derived from a linear codimension one Anosov diffeomorphism. Moreover, this system is intrinsically ergodic, and the A. Katok's conjecture about the existence of ergodic measures with intermediate entropies holds for it.

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来源期刊

Discrete and Continuous Dynamical Systems 数学-数学

CiteScore

2.50

自引率

0.00%

发文量

175

审稿时长

6 months

期刊介绍： DCDS, series A includes peer-reviewed original papers and invited expository papers on the theory and methods of analysis, differential equations and dynamical systems. This journal is committed to recording important new results in its field and maintains the highest standards of innovation and quality. To be published in this journal, an original paper must be correct, new, nontrivial and of interest to a substantial number of readers.