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Biological Research

versión impresa ISSN 0716-9760

Biol. Res. v.36 n.1 Santiago  2003 

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


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


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.



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


FERRARI P, MAASS A, MARTÍNEZ S, NEY P (2000) Cesàro mean distribution of group automata starting from measures with summable decay. Ergodic Theory and Dynamical Systems 20: 1657-1670         [ Links ]

KITCHENS B (1987) Expansive dynamics on zero-dimensional groups. Ergodic Theory and Dynamical Systems 7: 249-261         [ Links ]

LIND D (1984) Applications of ergodic theory and sofic systems to cellular automata. Physica D 10: 36-44         [ Links ]

MAASS A, MARTÍNEZ S (1998) On Cesàro limit distribution of a class of permutative cellular automata. Jrnl of Statist Phys 90: 435-452         [ Links ]

PIVATO M, YASSAWI R (2002) Limit Measures for Affine Cellular Automata, Ergodic Theory and Dynamical Systems 22: 1269-1287         [ Links ]

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