Evolution of probability measures by cellular automata on algebraic topological Markov chains.
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.
Maass
Alejandro
A
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.
Martínez
Servet
S
D000818:Animals; D005075:Biological Evolution; D019277:Entropy; D008390:Markov Chains; D008954:Models, Biological