关于r-中和熵：熵的公式及测度的存在性

IF 2.2 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2025-03-05 DOI:10.1007/s00220-025-05260-2

Changguang Dong, Qiujie Qiao

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引用次数: 0

摘要

在这篇文章中，我们研究了r中和局部熵，并推导出一些熵公式。我们证明，对于光滑系统的遍历双曲度量，r-中和局部熵等于布林-卡托克局部熵加上该度量点维的 r 倍。我们进一步证明了对于某些双曲系统，存在能使 r 中和熵最大化的遍历度量。此外，我们还构建了一个均匀双曲系统，对它来说，这种度量不是唯一的。最后，我们提出了与这些遍历度量相关的一些刚性结果。

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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On r-Neutralized Entropy: Entropy Formula and Existence of Measures Attaining the Supremum

In this article we study r-neutralized local entropy and derive some entropy formulas. For an ergodic hyperbolic measure of a smooth system, we show that the r-neutralized local entropy equals the Brin-Katok local entropy plus r times the pointwise dimension of the measure. We further establish the existence of ergodic measures that maximize the r-neutralized entropy for certain hyperbolic systems. Moreover, we construct a uniformly hyperbolic system, for which such measures are not unique. Finally, we present some rigidity results related to these ergodic measures.

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来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.