Related papers: Some properties of cellular automata with equicont…
We show that the set of strictly temporally periodic points of cellular automata with almost equicontinuous points is dense in the topological support of the measure. This extends a result of Lena, Margara and Dennunzio about the density of…
Revisiting the notion of m-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure m by iterations of a m-almost equicontinuous automata F, converges in Cesaro…
We show that a cellular automaton (or shift-endomorphism) on a transitive subshift is either almost equicontinuous or sensitive. On the other hand, we construct a cellular automaton on a full-shift (hence a transitive subshift) that is…
We are interested in topological and ergodic properties of one dimensional cellular automata. We show that an ergodic cellular automaton cannot have irrational eigenvalues. We show that any cellular automaton with an equicontinuous factor…
We study the set of strictly periodic points in surjective cellular automata, i.e., the set of those configurations which are temporally periodic for a given automaton but they not spatially periodic. This set turns out to be dense for…
Extending to all probability measures the notion of m-equicontinuous cellular automata introduced for Bernoulli measures by Gilman, we show that the entropy is null if m is an invariant measure and that the sequence of image measures of a…
Cellular automata, CA for short are continuous maps defined on the set of configurations over a finite alphabet A that commutes with the shift. They are characterized by the existence of local function which determine by local behavior the…
In this paper, we investigate some ergodic properties of $Z^{2}$-actions $T_{p,n}$ generated by an additive cellular automata and shift acting on the space of all doubly -infinitive sequences taking values in $Z_{m}$.
The concept of $\mu-$equicontinuity was introduced by Gilman to classify cellular automata. We show that under some conditions the sequence of Cesaro averages of a measure $\mu,$ converge under the actions of a $\mu -$equicontinuous CA. We…
The Besicovitch pseudodistance measures the relative size of the set of points where two functions take different values; the quotient space modulo the induced equivalence relation is endowed with a natural metric. We study the behavior of…
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…
We establish connections between several properties of topological dynamical systems, such as: - every point is generic for an ergodic measure, - the map sending points to the measures they generate is continuous, - the system splits into…
This paper studies directional dynamics in cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behaviour of a cellular automaton through the conjoint action of its global rule…
The trace subshift of a cellular automaton is the subshift of all possible columns that may appear in a space-time diagram, ie the infinite sequence of states of a particular cell of a configuration; in the language of symbolic dynamics one…
Following work by Hochman and Meyerovitch on multidimensional SFT, we give computability-theoretic characterizations of the real numbers that can appear as the topological entropies of one-dimensional and two-dimensional cellular automata.
We develop a rather elaborate computer program to investigate the jointly periodic points of one-dimensional cellular automata. The experimental results and mathematical context lead to questions, conjectures and a contextual theorem.
The aim of this article is to obtain a better understanding and classification of strictly ergodic topological dynamical systems with discrete spectrum. To that end, we first determine when an isomorphic maximal equicontinuous factor map of…
Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. With the goal to uncover different physically distinct classes of…
In this paper we are interested in the dynamical properties of a two dimensional cellular automaton that model the language shift in Algeria. We will study among other properties the surjectivity and the existence of equicontinuity points…
We study the behavior of probability measures under iteration of a surjective cellular automaton. We solve the following question in the negative: if the initial measure is ergodic and has full support, do all weak-* limit points of the…