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Articles, 5 records found

Articles	5 records found

18 p, 409.4 KB

Forward triplets and topological entropy on trees / Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Juher, David (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística) ; Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
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). [...]
2022 - DOI (Digital Object Identifier)

10.3934/dcds.2021131
Discrete and continuous dynamical systems. Series A, Vol. 42, Issue 2 (February 2022) , p. 623-641

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83 p, 5.0 MB

The period adding and incrementing bifurcations: from rotation theory to applications / Granados, Albert (Technical University of Denmark. Department of Applied Mathematics and Computer Science) ; Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Krupa, Maciej (Inria Sophia-Antipolis Research Center (França))
This survey article is concerned with the study of bifurcations of piecewise-smooth maps. We review the literature in circle maps and quasi-contractions and provide paths through this literature to prove sufficient conditions for the occurrence of two types of bifurcation scenarios involving rich dynamics. [...]
2017 - DOI (Digital Object Identifier)

10.1137/140996598
SIAM Review, Vol. 59 Núm. 2 (2017) , p. 225-292

Detailed record -

31 p, 570.9 KB

On the minimum positive entropy for cycles on trees / Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Juher, David (Universitat de Girona. Departament d'Informàtica i Matemàtica Aplicada) ; Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Consider, for any n ∈ N, the set Posn of all n-periodic tree patterns with positive topological entropy and the set Irrn ( Posn of all n-periodic irreducible tree patterns. The aim of this paper is to determine the elements of minimum entropy in the families Posn and Irrn. [...]
2017 - DOI (Digital Object Identifier)

10.1090/tran6677
Transactions of the American Mathematical Society, Vol. 369 Núm. 1 (2017) , p. 187-221

Detailed record -

38 p, 705.8 KB

Maximizing entropy of cycles on trees / Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Juher, David (Universitat de Girona. Departament d'Informàtica i Matemàtica Aplicada) ; King, Deborah M. (University of Melbourne. Departament of Mathematics and Statistics) ; Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we give a partial characterization of the periodic tree patterns of maximum entropy. More precisely, we prove that each periodic pattern with maximal entropy is irreducible and simplicial. [...]
2013 - DOI (Digital Object Identifier)

10.3934/dcds.2013.33.3237
Discrete and continuous dynamical systems. Series A, Vol. 33 Núm. 8 (2013) , p. 3237-3276

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27 p, 522.8 KB

Topological and algebraic reducibility for patterns on trees / Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Juher, David (Universitat de Girona. Departament d'Informàtica i Matemàtica Aplicada) ; Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
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. [...]
2015 - DOI (Digital Object Identifier)

10.1017/etds.2013.52
Ergodic Theory and Dynamical Systems, Vol. 35 (2015) , p. 34-63

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