GSD (Dynamical systems)

Dynamical systems is, and always has been, one of the main lines of research in Mathematics. It lies in the interest of all human civilizations to understand important questions such as the movement of the planets, the evolution of populations, or the discovery of chaotic dynamics in robust deterministic systems, which is why dynamical systems has become a major goal of study. After many years of evolution, the area of dynamical systems has undergone various transformations and developed branches to provide answers to questions of diverse nature.

The interests of the Dynamical Systems Group of UAB (GSD-UAB) can be described by stating our main research lines: Celestial Mechanics, Complex Dynamics, Discrete Real Dynamical Systems and Qualitative Theory of Differential Equations.

The members of our group work mainly in Catalonian universities (UAB, UB, UdG, UPC, URV, UVIC), although some of our researchers work in other universities in Spain and abroad. GSD-UAB collaborates with various national and international research groups.

Web page: http://www.gsd.uab.cat

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2019-05-16
15:36
19 p, 420.8 KB Phase portraits of continuous piecewise linear Liénard differential systems with three zones / Li, Shimin (Guangdong University of Finance and Economics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Phase portraits are an invaluable tool in studying differential systems. Most of known results about global phase portraits are related to the smooth differential systems. This paper deals with a class of planar continuous piecewise linear Liénard differential systems with three zones separated by two vertical lines without symmetry. [...]
2019 - 10.1016/j.chaos.2018.12.037
Chaos, solitons and fractals, Vol. 120 (March 2019) , p. 149-157  
2019-05-16
15:36
15 p, 434.9 KB New Family of Centers of Planar Polynomial Differential Systems of Arbitrary Even Degree / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mousavi, Marzieh (Isfahan University of Technology. Department of Mathematical Sciences) ; Nabavi, Arefeh (Isfahan University of Technology. Department of Mathematical Sciences)
The problem of distinguishing between a focus and a center is one of the classical problems in the qualitative theory of planar differential systems. In this paper, we provide a new family of centers of polynomial differential systems of arbitrary even degree. [...]
2019 - 10.1007/s10883-019-09432-x
Journal of Dynamical and Control Systems, (February 2019)  
2019-05-16
15:36
17 p, 389.6 KB Periodic solutions of linear, Riccati, and Abel dynamic equations / Bohner, Martin (Missouri S&T) ; Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
We study the number of periodic solutions of linear, Riccati and Abel dynamic equations in the time scales setting. In this way, we recover known results for corresponding differential equations and obtain new results for associated difference equations. [...]
2019 - 10.1016/j.jmaa.2018.10.018
Journal of mathematical analysis and applications, Vol. 470, Núm. 2 (February 2019) , p. 733-749  
2019-05-16
15:36
34 p, 632.0 KB Asymptotic Development of an Integral Operator and Boundedness of the Criticality of Potential Centers / Rojas, David (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística)
We study the asymptotic development at infinity of an integral operator. We use this development to give sufficient conditions to upper bound the number of critical periodic orbits that bifurcate from the outer boundary of the period function of planar potential centers. [...]
2019 - 10.1007/s10884-019-09753-2
Journal of dynamics and differential equations, (April 2019)  
2019-05-16
15:36
15 p, 488.5 KB On central configurations of the κn-body problem / Barrabés, Esther (Universitat de Girona) ; Cors, Josep Maria (Universitat Politècnica de Catalunya)
We consider planar central configurations of the Newtonian κn-body problem consisting in κ groups of regular n-gons of equal masses, called (κ,n)-crown. We derive the equations of central configurations for a general (κ,n)-crown. [...]
2019 - 10.1016/j.jmaa.2019.04.010
Journal of mathematical analysis and applications, Vol. 476, Núm. 2 (August 2019) , p. 720-736  
2019-05-16
15:36
29 p, 594.7 KB New lower bound for the Hilbert number in piecewise quadratic differential systems / Da Cruz, Leonardo Pereira Costa (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas (Brasil). Departamento de Matemática) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the number of limit cycles bifurcating from a piecewise quadratic system. All the differential systems considered are piecewise in two zones separated by a straight line. We prove the existence of 16 crossing limit cycles in this class of systems. [...]
2019 - 10.1016/j.jde.2018.09.032
Journal of differential equations, Vol. 266, Núm. 7 (March 2019) , p. 4170-4203  
2019-05-16
15:36
10 p, 613.0 KB Final evolutions for simplified multistrain/two-stream model for tuberculosis and dengue fever / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene D. S. (Universidade de São Paulo. Departamento de Matemática) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
The simplified multistrain/two-stream model for the tuberculosis and the Dengue fever here considered has three compartments, one susceptible and the other two infectious. We characterize all the final evolutions of this model under generic assumptions.
2019 - 10.1016/j.chaos.2018.11.022
Chaos, solitons and fractals, Vol. 118 (January 2019) , p. 181-186  
2019-05-16
15:36
7 p, 419.1 KB On the periods of a continuous self-map on a graph / Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena (Múrcia). Departamento de Matemática Aplicada y Estadística) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Let G be a graph and f be a continuous self-map on G. We present new and known results (from another point of view) on the periods of the periodic orbits of f using mainly the action of f on its homology, or the shape of the graph G.
2019 - 10.1007/s40314-019-0846-0
Computational & applied mathematics, Vol. 38, Issue 2 (June 2019) , art. 78  
2019-05-16
15:36
20 p, 1.7 MB A Route to Chaos in the Boros-Moll Map / Gardini, Laura (University of Urbino. Department of Economics Society Politics) ; Mañosa, Víctor (Universitat Politècnica de Catalunya. Departament de Matemàtiques) ; Sushko, Iryna (National Academy of Sciences of Ukraine)
The Boros-Moll map appears as a subsystem of a Landen transformation associated to certain rational integrals and its dynamics is related to their convergence. In the paper, we study the dynamics of a one-parameter family of maps which unfold the Boros-Moll one, showing that the existence of an unbounded invariant chaotic region in the Boros-Moll map is a peculiar feature within the family. [...]
2019 - 10.1142/S021812741930009X
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 29, Núm. 4 (April 2019) , art. 1930009  
2019-05-16
15:36
21 p, 428.1 KB Escaping points in the boundaries of Baker domains / Baranski, Krzysztof (University of Warsaw (Polònia). Institute of Mathematics) ; Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtiques i Informàtica) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtiques i Informàtica) ; Karpinska, Boguslawa (University of Warsaw (Polònia). Institute of Mathematics)
We study the dynamical behaviour of points in the boundaries of simply connected invariant Baker domains U of meromorphic maps f with a finite degree on U. We prove that if f $u is of hyperbolic or simply parabolic type, then almost every point in the boundary ofU,with respect to harmonicmeasure, escapes to infinity under iteration of f. [...]
2019 - 10.1007/s11854-019-0011-0
Journal d'Analyse Mathématique, Vol. 137, Issue 2 (March 2019) , p. 679-706