Topological and algebraic reducibility for patterns 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:	2015
Abstract:	We extend the classical notion of block structure for periodic orbits of interval maps to the setting of tree maps and study the algebraic properties of the Markov matrix of a periodic tree pattern having a block structure. We also prove a formula which relates the topological entropy of a pattern having a block structure with that of the underlying periodic pattern obtained by collapsing each block to a point, and characterize the structure of the zero entropy patterns in terms of block structures. Finally, we prove that an n-periodic pattern has zero (positive) entropy if and only if all n-periodic patterns obtained by considering the k-th iterate of the map on the invariant set have zero (respectively, positive) entropy, for each k relatively prime to n.
Grants:	Ministerio de Educación y Ciencia MTM2008-01486 Ministerio de Educación y Ciencia MTM2011-26995-C02-0
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Tree maps ; Patterns ; Topological entropy ; Block structure
Published in:	Ergodic Theory and Dynamical Systems, Vol. 35 (2015) , p. 34-63, ISSN 0143-3857

DOI: 10.1017/etds.2013.52

Postprint 27 p, 522.8 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
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