Topological and algebraic reducibility for patterns on trees
dc.contributor.author
dc.date.accessioned
2018-03-13T08:55:53Z
dc.date.available
2018-03-13T08:55:53Z
dc.date.issued
2015-02
dc.identifier.issn
0143-3857
dc.identifier.uri
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\mathrm{th} iterate of the map on the invariant set have zero (respectively, positive) entropy, for each k relatively prime to n
dc.description.sponsorship
The authors have been partially supported by MEC grant numbers MTM2008-01486 and MTM2011-26995-C02-01
dc.format.mimetype
application/pdf
dc.language.iso
eng
dc.publisher
Cambridge University Press (CUP)
dc.relation
MICINN/PN 2008-2010/MTM2008-01486
dc.relation.isformatof
Versió postprint del document publicat a: https://doi.org/10.1017/etds.2013.52
dc.relation.ispartof
© Ergodic Theory and Dynamical Systems, 2015, vol. 35, núm. 1, p. 34-63
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Articles publicats (D-IMA)
dc.rights
Tots els drets reservats
dc.title
Topological and algebraic reducibility for patterns on trees
dc.type
info:eu-repo/semantics/article
dc.rights.accessRights
info:eu-repo/semantics/openAccess
dc.type.version
info:eu-repo/semantics/acceptedVersion
dc.identifier.doi
dc.identifier.idgrec
023378
dc.contributor.funder
dc.type.peerreviewed
peer-reviewed
dc.identifier.eissn
1469-4417