Realization of Anosov diffeomorphisms on the torus

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-06-02 DOI:10.1112/jlms.70194

Tamara Kucherenko, Anthony Quas

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引用次数: 0

Abstract

We study area preserving Anosov maps on the two-dimensional torus within a fixed homotopy class. We show that the set of pressure functions for Anosov diffeomorphisms with respect to the geometric potential is equal to the set of pressure functions for the linear Anosov automorphism with respect to Hölder potentials. We use this result to provide a negative answer to the $C^{1 + α}$ version of the question posed by Rodriguez Hertz on whether two homotopic area-preserving $C^{\infty}$ Anosov diffeomorphisms whose geometric potentials have identical pressure functions must be $C^{\infty}$ conjugate.

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环面上Anosov微分同态的实现

研究了固定同伦类中二维环面上的保面积Anosov映射。我们证明了关于几何势的Anosov微分同构的压力函数集等于关于Hölder势的线性Anosov自同构的压力函数集。我们利用这一结果对Rodriguez Hertz关于两个同伦保面积C∞$C^\infty$ Anosov微分同态是否存在的问题的c1 + α $C^{1+\alpha }$版本提供了一个否定的答案其几何势具有相同的压力函数必须是C∞$C^\infty$共轭。

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

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.