Entropy bounds for endomorphisms commuting with K actions
by
Gary Morris
University of East Anglia
Coauthors: Tomm Ward

Shereshevsky has conjectured that a two dimensional cellular automata must have zero or infinite entropy. We prove a general result of this sort for endomorphisms commuting with a Z^2 action of completely positive entropy, which proves the conjecture of Shereshevsky for additive cellular automata. When the underlying group is connected, the result is related to Lehmer's problem. The method used in the cellular automata case also gives a proof of Shereshevsky's conjecture for a certain class of (non-additive) cellular automata.

Date received: February 25, 1998