Irrational eigenvalues of D-Dimensional Cellular automata
Dynamical Systems
2025-09-03 v1
Abstract
Cellular automata are dynamical systems defined on lattices and commuting with the Bernoulli shift. In this work, we focus on the spectral properties of D-dimensional cellular automata. We give a characterization of their spectrum from both topological and ergodic point of view. The main results of the paper show the impossibility for a cellular automaton with a fully blocking pattern to have a measurable irrational eigenvalues. Further more, a cellular automaton with a set of equicontinuity points of positive measure cannot have a measurable irrational eigenvalue.
Cite
@article{arxiv.2509.00933,
title = {Irrational eigenvalues of D-Dimensional Cellular automata},
author = {Nassima Ait Sadi and Rezki Chemlal},
journal= {arXiv preprint arXiv:2509.00933},
year = {2025}
}