Measure rigidity for algebraic bipermutative cellular automata
| dc.creator | Sablik, Mathieu | |
| dc.date | 2005-10-26 | |
| dc.date | 2006-01-24 | |
| dc.date.accessioned | 2026-07-07T06:47:56Z | |
| dc.date.available | 2026-07-07T06:47:56Z | |
| dc.description | Let $(\az,F)$ be a bipermutative algebraic cellular automaton. We present conditions which force a probability measure which is invariant for the $\N\times\Z$-action of $F$ and the shift map $\s$ to be the Haar measure on $\gs$, a closed shift-invariant subgroup of the Abelian compact group $\az$. This generalizes simultaneously results of B. Host, A. Maass and S. Mart\'ınez \cite{Host-Maass-Martinez-2003} and M. Pivato \cite{Pivato-2003}. This result is applied to give conditions which also force a $(F,\s)$-invariant probability measure to be the uniform Bernoulli measure when $F$ is a particular invertible expansive cellular automaton on $\an$. | |
| dc.identifier | https://arxiv.org/abs/math/0510564 | |
| dc.identifier | http://arxiv.org/abs/math/0510564 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103821 | |
| dc.subject | Dynamical Systems | |
| dc.title | Measure rigidity for algebraic bipermutative cellular automata | |
| dc.type | text |