dc.contributor.author |
Alsedà, L. |
dc.contributor.author |
Juher, D. |
dc.contributor.author |
Mañosas, F. |
dc.date.accessioned |
2023-06-19T11:09:55Z |
dc.date.available |
2023-06-19T11:09:55Z |
dc.date.issued |
2022-02-01 |
dc.identifier.uri |
http://hdl.handle.net/2072/535421 |
dc.description.sponsorship |
Ministerio de Economía y Competitividad, MINECO: MDM-2014-0445; Ministerio de Ciencia e Innovación, MICINN: 2017 SGR 1617 |
dc.format.extent |
18 p. |
dc.language.iso |
eng |
dc.publisher |
American Institute of Mathematical Sciences |
dc.rights |
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/ |
dc.source |
RECERCAT (Dipòsit de la Recerca de Catalunya) |
dc.subject.other |
Periodic patterns; Topological entropy; Tree maps |
dc.title |
FORWARD TRIPLETS AND TOPOLOGICAL ENTROPY ON TREES |
dc.type |
info:eu-repo/semantics/article |
dc.type |
info:eu-repo/semantics/acceptedVersion |
dc.embargo.terms |
cap |
dc.identifier.doi |
10.3934/dcds.2021131 |
dc.rights.accessLevel |
info:eu-repo/semantics/openAccess |
dc.description.abstract |
We provide a new and very simple criterion of positive topological entropy for tree maps. We prove that a tree map f has positive entropy if and only if some iterate fk has a periodic orbit with three aligned points consecutive in time, that is, a triplet (a, b, c) such that fk(a) = b, fk(b) = c and b belongs to the interior of the unique interval connecting a and c (a forward triplet of fk). We also prove a new criterion of entropy zero for simplicial n-periodic patterns P based on the non existence of forward triplets of fk for any 1 ≤ k < n inside P. Finally, we study the set Xn of all n-periodic patterns P that have a forward triplet inside P. For any n, we define a pattern that attains the minimum entropy in Xn and prove that this entropy is the unique real root in (1, ∞) of the polynomial xn − 2x − 1. © 2022 American Institute of Mathematical Sciences. All rights reserved. |