dc.contributor.author |
Alsedà i Soler, Lluís |
dc.contributor.author |
Juher, David |
dc.contributor.author |
Mañosas Capellades, Francesc |
dc.date |
2015 |
dc.identifier |
https://ddd.uab.cat/record/145364 |
dc.identifier |
urn:10.1017/etds.2013.52 |
dc.identifier |
urn:oai:ddd.uab.cat:145364 |
dc.identifier |
urn:gsduab:3395 |
dc.identifier |
urn:scopus_id:84920198795 |
dc.identifier |
urn:wos_id:000347162300002 |
dc.identifier |
urn:oai:egreta.uab.cat:publications/1943e25a-b9be-43e4-a889-041c13dfe040 |
dc.identifier |
urn:articleid:01433857v35p34 |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
|
dc.relation |
Ministerio de Educación y Ciencia MTM2008-01486 |
dc.relation |
Ministerio de Educación y Ciencia MTM2011-26995-C02-0 |
dc.relation |
Ergodic Theory and Dynamical Systems ; Vol. 35 (2015), p. 34-63 |
dc.rights |
open access |
dc.rights |
Tots els drets reservats. |
dc.rights |
https://rightsstatements.org/vocab/InC/1.0/ |
dc.subject |
Tree maps |
dc.subject |
Patterns |
dc.subject |
Topological entropy |
dc.subject |
Block structure |
dc.title |
Topological and algebraic reducibility for patterns on trees |
dc.type |
Article |
dc.description.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. |