{ "dc.contributor.author": "Alsedà, Lluís" , "dc.contributor.author": "Juher, David" , "dc.contributor.author": "Mañosas, Francesc" , "dc.date.accessioned": "2017-11-24T09:45:17Z" , "dc.date.available": "2017-11-24T09:45:17Z" , "dc.date.issued": "2017-01-01" , "dc.identifier.issn": "0002-9947 (versió paper)" , "dc.identifier.issn": "1088-6850 (versió electrònica)" , "dc.identifier.uri": "http://hdl.handle.net/10256/14607" , "dc.description.abstract": "Consider, for any n ∈ N, the set Pos n of all n-periodic tree patterns with positive topological entropy and the set Irr n ⊊ Pos n of all n-periodic irreducible tree patterns. The aim of this paper is to determine the elements of minimum entropy in the families Pos n and Irr n . Let λ n be the unique real root of the polynomial x n − 2x − 1 in (1, + ∞). We explicitly construct an irreducible n-periodic tree pattern Q n whose entropy is log(λ n ). For n = m k , where m is a prime, we prove that this entropy is minimum in the set Pos n . Since the pattern Q n is irreducible, Q n also minimizes the entropy in the family Irr n" , "dc.format.mimetype": "application/pdf" , "dc.language.iso": "eng" , "dc.publisher": "American Mathematical Society (AMS)" , "dc.relation.isformatof": "Versió postprint del document publicat a: https://doi.org/10.1090/tran6677" , "dc.relation.ispartof": "© Transactions of the American Mathematical Society, 2017, vol. 369, p. 187-221" , "dc.relation.ispartofseries": "Articles publicats (D-IMA)" , "dc.rights": "Tots els drets reservats" , "dc.subject": "Entropia topològica" , "dc.subject": "Topological entropy" , "dc.title": "On the minimum positive entropy for cycles on trees" , "dc.type": "info:eu-repo/semantics/article" , "dc.rights.accessRights": "info:eu-repo/semantics/openAccess" , "dc.type.version": "info:eu-repo/semantics/acceptedVersion" , "dc.identifier.doi": "https://doi.org/10.1090/tran6677" , "dc.identifier.idgrec": "025911" }