The canonical-boundary representation for automorphism groups of locally compact countable state Markov shifts
The aim of the present paper is to study the canonical-boundary representation of the automorphism groups of locally compact countable state Markov shifts. This conjugacy invariant homomorphism provides information about the symmetry of the Markov shift near its canonical boundary and gives which actions on the boundary can be realized by automorphisms. The author managed to introduce a new conjugacy invariant (the path structure at infinity -- a relation on the set of orbits of the canonical boundary) which is stronger than the canonical boundary and the periodic data at infinity. Furthermore it is determined its influence on the range of the canonical-boundary representation and the extendability of automorphisms from subsystems to the entire Markov shift.
scientific article; zbMATH DE number 5186280