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On the measure attractor of a cellular automaton

Pages: 524 - 535, Issue Special, August 2005

 Abstract        Full Text (275.4K)              

Petr Kůrka - Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic (email)

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.

Keywords:  Borel measures, signals, invariant subshifts, attractors.
Mathematics Subject Classification:  Primary: 58F11, 58F12; Secondary: 68Q80.

Received: September 2004;      Revised: April 2005;      Published: September 2005.