2006/09/01 by Hasan Akin, Akin, Hasan
Mathematics · #28D15 #37A15 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #math.DS #math.FA #msc:28D15 #msc:37A15
paper · pdf · doi:10.48550/arxiv.math/0609015
7 pages
arxiv created 2006/09/01 · arxiv updated 2009/12/01
In this paper we study the measure-theoretical entropy of the one-dimensional linear cellular automata (CA hereafter) Tf[-l,r], generated by local rule f(x-l,...,xr)= ∑i=-lrλixi(mod m), where l and r are positive integers, acting on the space of all doubly infinite sequences with values in a finite ring ℤm, m ≥ 2, with respect to a Markov measure. We prove that if the local rule f is bipermutative, then the measure-theoretical entropy of linear CA Tf[-l,r] with respect to a Markov measure μπP is h_μπP(Tf[-l,r])=-(l+r)∑i,j=0m-1pipijlog pij.