title: Evolution of probability measures by cellular automata on algebraic topological Markov chains.
abstract: In this paper we review some recent results on the evolution of probability measures under cellular automata acting on a fullshift. In particular we discuss the crucial role of the attractiveness of maximal measures. We enlarge the context of the results of a previous study of topological Markov chains that are Abelian groups; the shift map is an automorphism of this group. This is carried out by studying the dynamics of Markov measures by a particular additive cellular automata. Many of these topics were within the focus of Francisco Varela's mathematical interests.
authors.affiliation: Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático Departamento de Ingeniería Matemática, UMR 2071 UCHILE-CNRS, Universidad de Chile, Casilla 170-3, Correo 3, Santiago, Chile.
authors.forename: Alejandro
authors.initials: A
authors.lastname: Maass
authors.forename: Servet
authors.initials: S
authors.lastname: Martínez
mesh_terms: D000818:Animals; D005075:Biological Evolution; D019277:Entropy; D008390:Markov Chains; D008954:Models, Biological