# American Institute of Mathematical Sciences

2005, 2005(Special): 524-535. doi: 10.3934/proc.2005.2005.524

## On the measure attractor of a cellular automaton

 1 Faculty of Mathematics and Physics, Charles University in Prague

Received  September 2004 Revised  April 2005 Published  September 2005

Given a cellular automaton $F:A^{\ZZ} \to A^{\ZZ}$, we define its small quasi-attractor $\Qq_F$ as the nonempty intersection of all shift-invariant attractors of all $F^q\sigma^p$, where $q>0$ and $p\in\ZZ$. The measure attractor $\Mm_F$ is the closure of the supports of the members of the unique attractor of $F:\MMM_{\sigma}(A^{\ZZ}) \to \MMM_{\sigma}(A^{\ZZ})$ in the space of shift-invariant Borel probability measures.
Citation: Petr Kůrka. On the measure attractor of a cellular automaton. Conference Publications, 2005, 2005 (Special) : 524-535. doi: 10.3934/proc.2005.2005.524
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