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Considering the extension of an endomorphism to the completion, we count the number of orbits for the action of the subgroup of fixed points (respectively periodic) points on the set of infinite fixed (respectively periodic) points. Finally, we study the dynamics of infinite points: for automorphisms and some endomorphisms, defined in a precise way, fitting a classification given by Delgado and Ventura, we prove that every infinite point is either periodic or wandering, which implies that the dynamics is asymptotically periodic.<\/jats:p>","DOI":"10.1017\/s001309152200030x","type":"journal-article","created":{"date-parts":[[2022,8,12]],"date-time":"2022-08-12T10:49:31Z","timestamp":1660301371000},"page":"705-735","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":3,"title":["On the dynamics of extensions of free-abelian times free groups endomorphisms to the completion"],"prefix":"10.1017","volume":"65","author":[{"given":"Andr\u00e9","family":"Carvalho","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2022,8,12]]},"reference":[{"key":"S001309152200030X_ref11","unstructured":"11. Dugundji, J. , Topology, Reprinting of the 1966 original, Allyn and Bacon Series in Advanced Mathematics (Boston, MA-London-Sydney, Allyn and Bacon, Inc., 1978)."},{"key":"S001309152200030X_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(87)90004-1"},{"key":"S001309152200030X_ref20","doi-asserted-by":"publisher","DOI":"10.5802\/aif.1181"},{"key":"S001309152200030X_ref9","doi-asserted-by":"publisher","DOI":"10.1112\/jtopol\/jtu025"},{"key":"S001309152200030X_ref18","doi-asserted-by":"publisher","DOI":"10.1515\/jgth-2020-0034"},{"key":"S001309152200030X_ref21","doi-asserted-by":"publisher","DOI":"10.1515\/jgt-2012-0047"},{"key":"S001309152200030X_ref24","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2013.263.207"},{"key":"S001309152200030X_ref1","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2015.1094480"},{"key":"S001309152200030X_ref3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196716500028"},{"key":"S001309152200030X_ref22","unstructured":"22. 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