Evolution of probability measures by cellular automata on algebraic topological Markov chains
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Published on: April 1, 2012
Alejandro Maass1, Servet Martínez
1Departamento 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.
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.
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