Sensitivity–Chaos Equivalence in Linear Cellular Automata

IF 1.1 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Statistical Physics Pub Date : 2026-10-12 DOI:10.1007/s10955-026-03714-y

Chunlin Liu, Changlin Wang

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引用次数: 0

Abstract

We study the interplay between various notions of chaos for scalar linear cellular automata over \(\mathbb Z_m\). We show that the following properties are equivalent:

sensitivity (equivalently, the system is neither equicontinuous nor mean equicontinuous);
mean sensitivity (equivalently, k-sensitivity and k-mean sensitivity for every integer \(k\ge 2\));
Li–Yorke chaos (equivalently, mean Li–Yorke chaos and k-mean Li–Yorke sensitivity for every integer \(k\ge 2\));
the existence of a non-atomic ergodic invariant probability measure whose support contains the null configuration.

As a consequence, each such scalar linear cellular automaton is either equicontinuous (and hence mean equicontinuous) or simultaneously mean sensitive and Li–Yorke chaotic.

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线性元胞自动机的灵敏度-混沌等价

我们研究了\(\mathbb Z_m\)上标量线性元胞自动机的各种混沌概念之间的相互作用。我们证明了以下性质是等效的：灵敏度（等效地，系统既不是等连续的，也不是平均等连续的）；平均灵敏度（相当于每个整数的k灵敏度和k-均值灵敏度\(k\ge 2\)）；Li-Yorke混沌（即每个整数的平均Li-Yorke混沌和k-平均Li-Yorke灵敏度\(k\ge 2\)）；支持包含null配置的非原子遍历不变概率测度的存在性。因此，每个这样的标量线性元胞自动机要么是等连续的（因此是平均等连续的），要么同时是平均敏感和Li-Yorke混沌的。

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 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.