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Pàgina inicial > Articles > Articles publicats > Topological and algebraic reducibility for patterns on trees |
Data: | 2015 |
Resum: | 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. |
Ajuts: | Ministerio de Educación y Ciencia MTM2008-01486 Ministerio de Educación y Ciencia MTM2011-26995-C02-0 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Tree maps ; Patterns ; Topological entropy ; Block structure |
Publicat a: | Ergodic Theory and Dynamical Systems, Vol. 35 (2015) , p. 34-63, ISSN 0143-3857 |
Postprint 27 p, 522.8 KB |