Module Shifts and Measure Rigidity in Linear Cellular Automata
Dynamical Systems
2007-07-11 v1
Abstract
Suppose R is a finite commutative ring of prime characteristic, A is a finite R-module, M:=Z^D x N^E, and F is an R-linear cellular automaton on A^M. If mu is an F-invariant measure which is multiply shift-mixing in a certain way, then we show that mu must be the Haar measure on a coset of some submodule shift of A^M. Under certain conditions, this means mu must be the uniform Bernoulli measure on A^M.
Cite
@article{arxiv.0707.1408,
title = {Module Shifts and Measure Rigidity in Linear Cellular Automata},
author = {Marcus Pivato},
journal= {arXiv preprint arXiv:0707.1408},
year = {2007}
}
Comments
11 pages