Shifts on Compact and Discrete Lie Groups: Algebraic–Topological Invariants and Classification Problems

AbstractThis paper is devoted to an investigation of various dynamical concepts for group shift systems which are invariant by algebraic conjugacy (i.e., topological conjugacy preserving the group structure). The concept of controllability, which is stronger than topological transitivity, and the concept of limit dimension, which is analogous to topological entropy, are discussed at length. Particular attention is dedicated to the abelian case, for which duality results are also established