On the measure attractor of a cellular automaton

Petr Kůrka

doi:10.3934/proc.2005.2005.524

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2005, Volume 2005: 524-535. Doi: 10.3934/proc.2005.2005.524 open access

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On the measure attractor of a cellular automaton

Petr Kůrka^1,

1.
Faculty of Mathematics and Physics, Charles University in Prague

Received: September 2004

Revised: April 2005

Published: August 2005

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F11, 58F12; Secondary: 68Q80.

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