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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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2024-03-13
14:56
1 p, 214.3 KB Linealización en sistemas dinámicos holomorfos / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
2023
La Gaceta de la Real Sociedad Matemática Española, Vol. 26 Núm. 3 (2023) , p. 518  
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2024-03-11
10:46
On Families of Bowen - Series-Like Maps for Surface Groups / Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Juher, David (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística) ; Los, Jérôme ; Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We review some recent results on a class of maps, called Bowen - Series-like maps, obtained from a class of group presentations for surface groups. These maps are piecewise homeomorphisms of the circle with finitely many discontinuities. [...]
2023 - 10.1134/S1560354723040093
Regular and Chaotic Dynamics, Vol. 28, Issue 4-5 (October 2023) , p. 659-667  
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2024-03-11
10:45
24 p, 349.0 KB Three essays on Machin's type formulas / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Luca, Florian (Universidad Nacional Autónoma de México. Centro de Ciencias Matemáticas) ; Varona, Juan L. (Universidad de La Rioja. Departamento de Matemáticas y Computación)
We study three questions related to Machin's type formulas. The first one gives all two terms Machin formulas where both arctangent functions are evaluated 2-integers, that is values of the form b/2a for some integers a and b. [...]
2023 - 10.1016/j.indag.2023.07.002
Indagationes Mathematicae, Vol. 34, Issue 6 (November 2023) , p. 1373-1396  
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2024-03-08
10:55
Study of the Nonelementary Singular Points and the Dynamics Near the Infinity in Predator-Prey Systems / Diz-Pita, Érika (Universidade de Santiago de Compostela) ; Llibre, Jaume (Universitat Autònoma de Barcelona) ; Otero-Espinar, M. Victoria (Universidade de Santiago de Compostela)
In this chapter, we present the results obtained in two predator-prey systems, paying special attention to the dynamics near the infinity and the nonelementary singular points. First, the desingularization technique known as blow-up technique allows one to study any type of singularities of analytic systems in dimension two even if they are not elementary. [...]
Cham : Springer, 2023 (Nonlinear Systems and Complexity ; 38) - 10.1007/978-3-031-42689-6_5
Computational and Mathematical Models in Biology, 2023, p. 103-128  
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2024-03-08
10:55
9 p, 290.7 KB Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vulpe, Nicolae (Vladimir Andrunakievichi Institute of Mathematics and Computer Science (Moldova))
The following differential quadratic polynomial differential system dx/dt=y−x, dy/dt=2y−y/y−1(2−yy−5y−4/y−1x), when the parameter y∈(1,2] models the structure equations of an isotropic star having a linear barotropic equation of state, being x=m(r)/r where m(r)≥0 is the mass inside the sphere of radius r of the star, y=4πr2ρ where ρ is the density of the star, and t=ln(r/R) where R is the radius of the star. [...]
2024 - 10.3390/appliedmath4010004
AppliedMath, Vol. 4, Issue 1 (January 2024) , p. 70-78  
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2024-03-08
10:55
36 p, 567.3 KB Oscil·ladors en ressonància / Rojas, David (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística)
Un oscil·lador és un sistema en el qual tots els moviments possibles són periòdics. Si aquest període és comú per a tots els moviments, es diu que l'oscil·lador és isòcron. Quan el sistema és forçat per una pertorbació periòdica amb el mateix període, la dinàmica pot canviar dràsticament i el fenomen de ressonància pot aparèixer. [...]
2022 - 10.2436/20.2002.01.105
Butlletí de la Societat Catalana de Matemàtiques, Vol. 37, Núm. 2 (2022) , p. 137-172  
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2024-02-28
05:39
20 p, 971.1 KB Planar central configurations of some restricted (4 + 1)-body problems / Corbera Subirana, Montserrat (Universitat de Vic - Universitat Central de Catalunya. Departament d'Enginyeries) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We start with the 13 central configurations of the restricted (4 + 1) body problem having four primaries with equal masses at the vertices of a square. Then, we describe the evolution of these central configurations when some of the masses of the four primaries tend to zero and the remainder ones keep constant. [...]
2022 - 10.1063/5.0091642
Journal of Mathematical Physics, Vol. 63, Issue 12 (December 2022) , art. 122901  
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2024-02-27
14:59
Critical periods in planar polynomial centers near a maximum number of cusps / De Maesschalck, Peter (Hasselt University) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide the best lower bound for the number of critical periods of planar polynomial centers known up to now. The new lower bound is obtained in the Hamiltonian class and considering a single period annulus. [...]
2024 - 10.1016/j.jde.2023.10.034
Journal of differential equations, Vol. 380 (January 2024) , p. 181-197  
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2024-02-27
14:59
10 p, 616.4 KB Integrability and dynamics of a simplified class B laser system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
A simplified class B laser system is a family of differential polynomial systems of degree two depending on the parameters a and b. Its rich dynamics has already been observed in 1980s, see Arecchi et al. [...]
2023 - 10.1063/5.0169342
Chaos, Vol. 33, Issue 10 (October 2023) , art. 103119  
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2024-02-27
14:59
24 p, 449.0 KB Probability of existence of limit cycles for a family of planar systems / Coll, Bartomeu (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
The goal of this work is the study of the probability of occurrence of limit cycles for a family of planar differential systems that are a natural extension of linear ones. To prove our results we first develop several results of non-existence, existence, uniqueness and non-uniqueness of limit cycles for this family. [...]
2023 - 10.1016/j.jde.2023.07.015
Journal of differential equations, Vol. 373 (November 2023) , p. 152-175  
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