Mathematics – Dynamical Systems
Scientific paper
2001-08-12
Mathematics
Dynamical Systems
LaTeX2E Format, 20 pages, 1 LaTeX figure, 2 EPS figures, to appear in Ergodic Theory and Dynamical Systems, submitted April 20
Scientific paper
If M is a monoid (e.g. the lattice Z^D), and A is an abelian group, then A^M is a compact abelian group; a linear cellular automaton (LCA) is a continuous endomorphism F:A^M --> A^M that commutes with all shift maps. If F is diffusive, and mu is a harmonically mixing (HM) probability measure on A^M, then the sequence {F^N mu} (N=1,2,3,...) weak*-converges to the Haar measure on A^M, in density. Fully supported Markov measures on A^Z are HM, and nontrivial LCA on A^{Z^D} are diffusive when A=Z/p is a prime cyclic group. In the present work, we provide sufficient conditions for diffusion of LCA on A^{Z^D} when A=Z/n is any cyclic group or when A=[Z/(p^r)]^J (p prime). We show that any fully supported Markov random field on A^{Z^D} is HM (where A is any abelian group).
Pivato Marcus
Yassawi Reem
No associations
LandOfFree
Limit Measures for Affine Cellular Automata, II does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Limit Measures for Affine Cellular Automata, II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Limit Measures for Affine Cellular Automata, II will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-626987