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

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 cha...

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Main Authors: ALEJANDRO MAASS, SERVET MARTÍNEZ
Format: Article
Language:English
Published: BMC 2003-01-01
Series:Biological Research
Online Access:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-97602003000100010
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spelling doaj-6742ac0de29d453dbdb4a3aadf0785cc2020-11-25T01:30:46ZengBMCBiological Research0716-97600717-62872003-01-01361113118Evolution of probability measures by cellular automata on algebraic topological Markov chainsALEJANDRO MAASSSERVET MARTÍNEZIn 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.http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-97602003000100010
collection DOAJ
language English
format Article
sources DOAJ
author ALEJANDRO MAASS
SERVET MARTÍNEZ
spellingShingle ALEJANDRO MAASS
SERVET MARTÍNEZ
Evolution of probability measures by cellular automata on algebraic topological Markov chains
Biological Research
author_facet ALEJANDRO MAASS
SERVET MARTÍNEZ
author_sort ALEJANDRO MAASS
title Evolution of probability measures by cellular automata on algebraic topological Markov chains
title_short Evolution of probability measures by cellular automata on algebraic topological Markov chains
title_full Evolution of probability measures by cellular automata on algebraic topological Markov chains
title_fullStr Evolution of probability measures by cellular automata on algebraic topological Markov chains
title_full_unstemmed Evolution of probability measures by cellular automata on algebraic topological Markov chains
title_sort evolution of probability measures by cellular automata on algebraic topological markov chains
publisher BMC
series Biological Research
issn 0716-9760
0717-6287
publishDate 2003-01-01
description 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.
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-97602003000100010
work_keys_str_mv AT alejandromaass evolutionofprobabilitymeasuresbycellularautomataonalgebraictopologicalmarkovchains
AT servetmartinez evolutionofprobabilitymeasuresbycellularautomataonalgebraictopologicalmarkovchains
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