Pseudo-Orbit Tracing and Algebraic actions of countable amenable groups

Tom Meyerovitch

Published 2017-01-05Version 1

We prove that every expansive action of an amenable group with positive entropy that has the pseudo-orbit tracing property admits off-diagonal asymptotic pairs. Other implications of the pseudo-orbit tracing property for group actions are presented. Using Chung and Li's algebraic characterization of expansiveness, we prove obtain the pseudo-orbit tracing property for a class of expansive algebraic actions. This class includes every expansive principle algebraic action of a countable group. We also construct a expansive homeomorphisms and expansive algebraic actions of (non-finitely generated) abelian groups having positive topological entropy and no off-diagonal asymptotic pairs. This complements a result and answers a question of Chung and Li.