Hierarchical Structure of Periodic Orbits of a Hyperbolic Automorphism on the 2-Torus

IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Journal of Statistical Physics Pub Date : 2025-02-05 DOI:10.1007/s10955-025-03403-2
Huynh M. Hien, Nguyen B. Tran, Tran N. Nguyen
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Abstract

This paper studies the hierarchical structure of periodic orbits of the automorphism induced by the matrix \(A=\begin{pmatrix} 2& 1\\ 1& 1 \end{pmatrix}\) on the torus \({\mathbb {T}}^2\). The induced symbolic dynamics is not trivial with forbidden sequences. We show that the periodic orbits of the system is hierarchically structured by clusters. We establish the number of clusters via symbolic dynamics and digraphs. Algorithms that group all periodic orbits in clusters are given.

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本文研究了矩阵\(A=\begin{pmatrix} 2& 1\ 1& 1\end{pmatrix}\) 在环面\({\mathbb {T}}^2\) 上诱导的自动态周期轨道的层次结构。诱导的符号动力学与禁止序列无关。我们证明了系统的周期轨道是由簇分层结构的。我们通过符号动力学和数字图确定了簇的数量。我们还给出了将所有周期轨道归为簇的算法。
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来源期刊
Journal of Statistical Physics
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.
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