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On the minimum positive entropy for cycles on trees

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

American Mathematical Society (AMS)

Author: Alsedà i Soler, Lluís
Juher, David
Mañosas, Francesc
Date: 2017 January 1
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
Format: application/pdf
Document access: http://hdl.handle.net/10256/14607
Language: eng
Publisher: American Mathematical Society (AMS)
Collection: info:eu-repo/semantics/altIdentifier/doi/10.1090/tran6677
info:eu-repo/semantics/altIdentifier/issn/0002-9947
info:eu-repo/semantics/altIdentifier/eissn/1088-6850
Rights: Tots els drets reservats
Subject: Entropia topològica
Topological entropy
Title: On the minimum positive entropy for cycles on trees
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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