arXiv Analytics

Sign in

arXiv:math/0603326 [math.DS]AbstractReferencesReviewsResources

Right-Permutative Cellular Automata on Topological Markov Chains

Marcelo Sobottka

Published 2006-03-14, updated 2017-02-14Version 4

In this paper we consider cellular automata $(\mathfrak{G},\Phi)$ with algebraic local rules and such that $\mathfrak{G}$ is a topological Markov chain which has a structure compatible to this local rule. We characterize such cellular automata and study the convergence of the Ces\`aro mean distribution of the iterates of any probability measure with complete connections and summable decay.

Comments: 16 pages, 2 figure. A new version with improved redaction of Theorem 6.3(i)) to clearify its consequences
Journal: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, Volume 20, Number 4, April 2008, pp. 1095--1109
Categories: math.DS, math.PR
Subjects: 37B15, 54H20
Related articles: Most relevant | Search more
arXiv:1110.2942 [math.DS] (Published 2011-10-13, updated 2012-10-21)
An extension of Kesten's criterion for amenability to topological Markov chains
arXiv:1302.4091 [math.DS] (Published 2013-02-17, updated 2013-06-29)
SL(2,R)-invariant probability measures on the moduli spaces of translation surfaces are regular
arXiv:1806.00214 [math.DS] (Published 2018-06-01)
Topological Markov chains of given entropy and period with or without measure of maximal entropy

Links

Toolbox