GSD (Grup de Sistemes Dinàmics)

Els sistemes dinàmics són, i sempre han estat, una de les principals línies d'investigació en Matemàtiques. És interès de totes les civilitzacions humanes comprendre qüestions importants, com el moviment dels planetes, l'evolució de les poblacions, o l'estudi de la dinàmica en sistemes deterministes, de manera que els sistemes dinàmics s'han convertit en un objectiu important d'estudi. Després de molts anys d'evolució, l'àrea dels sistemes dinàmics ha sofert diverses transformacions i ha desenvolupat diverses branques que han permès respondre preguntes de diversa índole.

Les linies principals d'investigació del Grup de Sistemes Dinàmics de la UAB (GSD-UAB) són: Mecànica celeste, Dinàmica complexa, Sistemes Dinàmics discrets i Teoria qualitativa d'equacions diferencials.

Els membres del nostre grup treballen principalment a les universitats catalanes (UAB, UB, UdG, UPC, URV, UVic), tot i que alguns dels nostres investigadors treballen en altres universitats d'Espanya i a l'estranger. El GSD-UAB col·labora asiduament amb diversos grups de recerca nacionals i internacionals.

Pàgina web: http://www.gsd.uab.cat

Estadístiques d'ús Els més consultats
Darreres entrades:
2023-09-05
12:41
On the indices of singular points for planar bounded piecewise smooth polynomial vector field / Li, Shimin (Hangzhou Normal University. School of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Sun, Xianbo (Hangzhou Normal University. School of Mathematics)
We prove that for any piecewise-smooth bounded polynomial vector field in R2 with finitely many finite H-singular points (which include singular points, hyperbolic pseudo-equilibria and two fold singularities), the sum of the indices of all its finite H-singular points is 1.
2023 - 10.1016/j.nahs.2023.101350
Nonlinear Analysis: Hybrid Systems, Vol. 49 (August 2023) , art. 101350  
2023-09-05
12:41
8 p, 1.6 MB Social copying drives a tipping point for nonlinear population collapse / Oro, Daniel (Centre d'Estudis Avançats de Blanes. Laboratori d'Ecologia Teòrica i Computacional - CSIC) ; Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Hastings, Alan (University of California. Department of Environmental Science and Policy) ; Genovart, Meritxell (Centre d'Estudis Avançats de Blanes. Laboratori d'Ecologia Teòrica i Computacional - CSIC) ; Sardanyés, Josep (Centre de Recerca Matemàtica)
Sudden changes in populations are ubiquitous in ecological systems, especially under perturbations. The agents of global change may increase the frequency and severity of anthropogenic perturbations, but complex populations' responses hamper our understanding of their dynamics and resilience. [...]
2023 - 10.1073/pnas.2214055120
Proceedings of the National Academy of Sciences of the United States of America, Vol. 120, Issue 11 (March 2023) , art. e2214055120  
2023-09-05
12:41
11 p, 281.1 KB Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line / Bastos, Jefferson L. R. (Universidade Estadual Paulista. Departamento de Matemática) ; Buzzi, Claudio (Universidade Estadual Paulista. Departamento de Matemática) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we recover the best lower bound for the number of limit cycles in the planar piecewise linear class when one vector field is defined in the first quadrant and a second one in the others. [...]
2023 - 10.1007/s12346-023-00817-9
Qualitative Theory of Dynamical Systems, Vol. 22, Issue 4 (December 2023) , art. 125  
2023-09-05
12:41
Nonexistence and Uniqueness of Limit Cycles in a Class of Three-Dimensional Piecewise Linear Differential Systems / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics) ; Huang, Lihong (Changsha University. College of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
During the last twenty years there has been increasing interest in studying the piecewise differential systems, mainly due to their many applications in natural science and technology. Up to now the most studied differential systems are in dimension two, here we study them in dimension three. [...]
2023 - 10.1142/S021812742350075X
International Journal of Bifurcation and Chaos, Vol. 33, Issue 6 (May 2023) , art. 2350075  
2023-09-05
12:41
Limit cycles of a continuous piecewise differential system formed by a quadratic center and two linear centers / Anacleto, Maria Elisa (Universidad del Bío-Bío. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)
The study of limit cycles of planar differential systems is one of the main and difficult problems for understanding their dynamics. Thus the objective of this paper is to study the limit cycles of continuous piecewise differential systems in the plane separated by a non-regular line Σ. [...]
2023 - 10.1007/s40590-023-00501-7
Boletin de la Sociedad Matematica Mexicana, Vol. 29, Issue 2 (July 2023) , art. 29  
2023-09-05
12:41
35 p, 627.1 KB Criteria on the existence of limit cycles in planar polynomial differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Grau, Maite (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We summarize known criteria for the non-existence, existence and on the number of limit cycles of autonomous real planar polynomial differential systems, and also provide new results. We give examples of systems which realize the maximum number of limit cycles provided by each criterion. [...]
2022 - 10.1016/j.exmath.2022.09.002
Expositiones Mathematicae, Vol. 40, Issue 4 (December 2022) , p. 1049-1083  
2023-09-05
12:41
On the Periodic Orbits of the Perturbed Two- and Three-Body Problems / Abouelmagd, Elbaz I. (National Research Institute of Astronomy and Geophysics. Astronomy Department (Egypt)) ; Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena. Departamento de Matemática Aplicada y Estadística) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this work, a perturbed system of the restricted three-body problem is derived when the perturbation forces are conservative alongside the corresponding mean motion of two primaries bodies. Thus, we have proved that the first and second types of periodic orbits of the rotating Kepler problem can persist for all perturbed two-body and circular restricted three-body problems when the perturbation forces are conservative or the perturbed motion has its own extended Jacobian integral.
2023 - 10.3390/galaxies11020058
Galaxies, Vol. 11, Issue 2 (April 2023) , art. 58  
2023-09-05
12:41
On the C1 non-integrability of the autonomous differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In the study of the dynamics of the autonomous differential systems to know the existence or non-existence of first integrals is a relevant fact. These last decades the meromorphic non-integrability of the autonomous differential systems have been studied intensively using the Ziglin's and the Morales-Ramis' theories. [...]
2023 - 10.1016/j.nonrwa.2023.103943
Nonlinear Analysis: Real World Applications, Vol. 74 (December 2023) , art. 103943  
2023-09-05
12:41
28 p, 2.1 MB Dynamics of Newton-like root finding methods / Campos, Beatriz (Universitat Jaume I. Instituto de Matemáticas y Aplicaciones de Castellón) ; Canela Sánchez, Jordi (Universitat Jaume I. Institut Universitari de Matemátiques i Aplicacions de Castelló) ; Vindel, Pura (Universitat Jaume I. Instituto de Matemáticas y Aplicaciones de Castellón)
When exploring the literature, it can be observed that the operator obtained when applying Newton-like root finding algorithms to the quadratic polynomials z − c has the same form regardless of which algorithm has been used. [...]
2023 - 10.1007/s11075-022-01474-w
Numerical Algorithms, Vol. 93, Issue 4 (August 2023) , p. 1453-1480  
2023-09-05
12:41
Invariants of polynomial vector fields / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We characterize the existence of first integrals and invariants (first integrals depending on the time) for the polynomial vector fields which are invariant under an involution.
2023 - 10.1016/j.jde.2023.05.024
Journal of differential equations, Vol. 365 (August 2023) , p. 895-904