Sofic subshifts and piecewise isometric systems
by
Arek Goetz
Boston University

We study the natural symbolic dynamics associated with piecewise continuous , not necessarily invertible dynamical systems. Our study is centered primarily on the relationship between the point-set topological properties of the partition and the symbolic coding. We prove that for a class of maps locally preserving distances with regular partition, all almost sofic subshift embeddings have zero entropy. However, in Euclidean spaces, there are examples of systems with non-regular partition for which the coding maps can be surjective, in particular embedding all sofic subshifts.

Date received: February 16, 1998