2026-04-18T01:07:12Zhttps://recercat.cat/oai/request

oai:recercat.cat:10256/151382024-06-18T12:17:20Zcom_2072_452955com_2072_2054col_2072_453069

2024-06-18T12:17:20Z urn:hdl:10256/15138 Topological and algebraic reducibility for patterns on trees Alsedà i Soler, Lluís Juher, David Mañosas, Francesc Arbres (Teoria de grafs) Trees (Graph theory) Topologia algebraica Algebraic topology 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\mathrm{th} iterate of the map on the invariant set have zero (respectively, positive) entropy, for each k relatively prime to n The authors have been partially supported by MEC grant numbers MTM2008-01486 and MTM2011-26995-C02-01 2024-06-18T12:17:20Z 2024-06-18T12:17:20Z 2015-02 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion peer-reviewed http://hdl.handle.net/10256/15138 info:eu-repo/semantics/altIdentifier/doi/10.1017/etds.2013.52 info:eu-repo/semantics/altIdentifier/issn/0143-3857 info:eu-repo/semantics/altIdentifier/eissn/1469-4417 MICINN/PN 2008-2010/MTM2008-01486 Tots els drets reservats info:eu-repo/semantics/openAccess Cambridge University Press (CUP) © Ergodic Theory and Dynamical Systems, 2015, vol. 35, núm. 1, p. 34-63 Articles publicats (D-IMA)