Right-permutative cellular automata on topological Markov chains | Zendy

Marcelo Sobottka | Zendy

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Right-permutative cellular automata on topological Markov chains

Author(s) -

Marcelo Sobottka

Publication year - 2008

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2008.20.1095

Subject(s) - cellular automaton , markov chain , iterated function , mathematics , algebraic number , continuous spatial automaton , convergence (economics) , measure (data warehouse) , algebraic structure , discrete mathematics , topology (electrical circuits) , combinatorics , computer science , automaton , quantum finite automata , pure mathematics , theoretical computer science , algorithm , automata theory , statistics , database , mathematical analysis , economics , economic growth

In this paper we consider cellular automata $(\mathfrak{G},\Phi)$ withalgebraic local rules and such that $\mathfrak{G}$ is a topological Markovchain which has a structure compatible to this local rule. We characterize suchcellular automata and study the convergence of the Ces\`aro mean distributionof the iterates of any probability measure with complete connections andsummable decay.Comment: 16 pages, 2 figure. A new version with improved redaction of Theorem 6.3(i)) to clearify its consequence

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