On the minimum positive entropy for cycles on trees
Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Juher, David (Universitat de Girona. Departament d'Informàtica i Matemàtica Aplicada)
Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2017
Abstract:	Consider, for any n ∈ N, the set Posn of all n-periodic tree patterns with positive topological entropy and the set Irrn ( Posn of all n-periodic irreducible tree patterns. The aim of this paper is to determine the elements of minimum entropy in the families Posn and Irrn. Let λn be the unique real root of the polynomial xn − 2x − 1 in (1, +∞). We explicitly construct an irreducible n-periodic tree pattern Qn whose entropy is log(λn). For n = mk, where m is a prime, we prove that this entropy is minimum in the set Posn. Since the pattern Qn is irreducible, Qn also minimizes the entropy in the family Irrn.
Grants:	Ministerio de Economía y Competitividad MTM2008-01486 Ministerio de Economía y Competitividad MTM2011-26995-C02-01
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Tree maps ; Periodic patterns ; Topological entropy
Published in:	Transactions of the American Mathematical Society, Vol. 369 Núm. 1 (2017) , p. 187-221, ISSN 1088-6850

DOI: 10.1090/tran6677

Postprint 31 p, 570.9 KB

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