随机环面映射的旋转熵

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Statistical Physics Pub Date : 2025-04-21 DOI:10.1007/s10955-025-03443-8

Weifeng Jiang, Zhengxing Lian, Yujun Zhu

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引用次数: 0

摘要

本文研究了环面上随机动力系统\(\varphi \)的旋转熵\(h_r(\varphi )\)。对于满足一定假设的\(\varphi \)，得到了\(h_r(\varphi )\)的公式，对于更一般的\(\varphi \)，给出了\(h_r(\varphi )\)的下界和上界。几个例子表明，如果没有这些假设，这些结果可能不成立。这项工作可以看作是之前的工作（Jiang等人在J Differ Equ 379:862-883, 2024）的随机版本，其中引入了旋转熵，并将其作为任何环面映射的同伦不变量进行了研究。

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Rotational Entropy for Random Torus Maps

In this paper, the rotational entropy \(h_r(\varphi )\) is investigated for a random dynamical system \(\varphi \) on the torus. The formula of \(h_r(\varphi )\) is obtained for \(\varphi \) which satisfies certain assumptions, and the lower and upper bounds of \(h_r(\varphi )\) are given for more general \(\varphi \). Several examples are presented to show that these results may not hold without the assumptions. This work can be seen as a random version of the previous work (Jiang et al. in J Differ Equ 379:862–883, 2024), in which the rotational entropy was introduced and investigated as a homotopy invariant for any torus map.

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来源期刊

Journal of Statistical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

12.50%

发文量

152

审稿时长

3-6 weeks

期刊介绍： The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.