关于海森堡群作用在环上的熵的说明

IF 0.8 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2024-07-10 DOI:10.1007/s10114-024-3076-3

Yu Zhang, Yu Jun Zhu

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引用次数: 0

摘要

本文研究离散海森堡群作用的熵。本文引入了两种熵：\(\tilde{h}(\alpha)\)和 h(α)，其中\(\tilde{h}(\alpha)\)是按照鲁埃尔的方法定义的，而 h(α)是通过α的自然扩展定义的。研究表明，当 X 是环且 α 由整数矩阵诱导时，\(\tilde{h}(\alpha)\) 为零，而 h(α) 可以通过矩阵的特征值来表示。

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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A Note on the Entropy for Heisenberg Group Actions on the Torus

In this paper, the entropy of discrete Heisenberg group actions is considered. Let α be a discrete Heisenberg group action on a compact metric space X. Two types of entropies, \(\tilde{h}(\alpha)\) and h(α) are introduced, in which \(\tilde{h}(\alpha)\) is defined in Ruelle’s way and h(α) is defined via the natural extension of α. It is shown that when X is the torus and α is induced by integer matrices then \(\tilde{h}(\alpha)\) is zero and h(α) can be expressed via the eigenvalues of the matrices.

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.