On Kůrka's dichotomy for cellular automata on groups

HAL 2026 Preprint Open access

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Authors: Jade Angela Hope Audouard, Guillaume Theyssier
Cited by: 0

Abstract

This paper is about topological dynamics of cellular automata on finitely generated groups. We tackle the problem of determining for which group sensitivity to initial conditions is equivalent to the absence of equicontinuity points (so-called Kůrka's dichotomy). We show that the dichotomy holds on any virtually-Z group but not on free groups with 2 or more generators. We also show that if it holds on some group, it must hold on any of its subgroups.

Fields of Study & Subjects

Cellular Automata and Applications Mathematical Dynamics and Fractals Advanced Topology and Set Theory

Publication details

Journal / source
HAL
Publication date
23 February 2026
Language
EN
Document type
Preprint