{ "id": "1701.01318", "version": "v1", "published": "2017-01-05T13:59:57.000Z", "updated": "2017-01-05T13:59:57.000Z", "title": "Pseudo-Orbit Tracing and Algebraic actions of countable amenable groups", "authors": [ "Tom Meyerovitch" ], "comment": "21 pages", "categories": [ "math.DS" ], "abstract": "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.", "revisions": [ { "version": "v1", "updated": "2017-01-05T13:59:57.000Z" } ], "analyses": { "subjects": [ "22D40", "37B05", "37B40" ], "keywords": [ "algebraic action", "countable amenable groups", "pseudo-orbit tracing property", "tracing property admits off-diagonal", "property admits off-diagonal asymptotic pairs" ], "note": { "typesetting": "TeX", "pages": 21, "language": "en", "license": "arXiv", "status": "editable" } } }