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Biological Research

versión impresa ISSN 0716-9760

Biol. Res. v.36 n.1 Santiago  2003

http://dx.doi.org/10.4067/S0716-97602003000100010 

Evolution of probability measures by cellular automata on algebraic topological Markov chains

ALEJANDRO MAASS and SERVET MARTÍNEZ

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

Corresponding Author: Servet Martínez
e-mail: smartine@dim.uchile.cl

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.

Key terms: Topological Markov chains, cellular automata, maximal measure, entropy, additive cellular automata.

 

ACKNOWLEDGMENTS

The authors acknowledge financial support from Millennium Nucleus Information and Randomness ICM P01-005.

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