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

Darreres entrades:
2017-04-07
22:36
On the Chebyshev property of certain abelian integrals near a polycycle / Marín Pérez, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Villadelprat, Jordi (Universitat Rovira i Virgili. Departament d’Enginyeria Informàtica i Matemàtiques)
F. Dumortier and R. Roussarie formulated in [Birth of canard cycles, Discrete Contin. Dyn. Syst. 2 (2009) 723–781] a conjecture concerning the Chebyshev property of a collection I0; I1; : : : ; In of Abelian integrals arising from singular perturbation problems occurring in planar slow-fast systems. [...]
2017 - 10.1007/s12346-017-0226-3
Qualitative Theory of Dynamical Systems, 2017, p. 1-10  
2017-01-23
16:21
8 p, 341.6 KB Uniform isochronous cubic and quartic centers: Revisited / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we completed the classification of the phase portraits in the Poincaré disc of uniform isochronous cubic and quartic centers previously studied by several authors. There are three and fourteen different topological phase portraits for the uniform isochronous cubic and quartic centers respectively.
2017
Journal of Computational and Applied Mathematics, Vol. 313 (2017) , p. 448-453  
2017-01-23
16:21
16 p, 437.4 KB Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory / Benterki, Rebiha (Centre Universitaire de Bordj Bou Arréridj(Algeria). Département de Mathématiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we classify the phase portraits in the Poincar\'e disc of the centers of the generalized class of Kukles systems \[ =-y,=x ax^3y bxy^3, \] symmetric with respect to the y-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the periodic solutions of these centers when we perturb them inside the class of all polynomial differential systems of degree 4.
2017 - 10.1016/j.cam.2016.08.047
Journal of Computational and Applied Mathematics, Vol. 313 (2017) , p. 273-283  
2017-01-23
16:21
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, 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
Transactions of the American Mathematical Society, Vol. 369 Núm. 1 (2017) , p. 187-221  
2017-01-23
16:21
27 p, 505.8 KB Topological Classification of Quadratic Polynomial Differential Systems with a Finite Semi-Elemental Triple Saddle / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene D. S. (Universidade de Sâo Paulo(Brazil). Departamento de Matemática) ; Rezende, Alex Carlucci (Universidade de Sâo Paulo(Brazil). Departamento de Matemática)
The study of planar quadratic differential systems is very important not only because they appear in many areas of applied mathematics but due to their richness in structure, stability and questions concerning limit cycles, for example. [...]
2016 - 10.1142/S0218127416501881
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 26 Núm. 11 (2016) , p. 1650188 (26 pages)  
2017-01-23
16:21
13 p, 299.6 KB On a Class of Invariant Algebraic Curves for Kukles Systems / Osuna, Osvaldo (UMSNH(México). Instituto de Física y Matemáticas) ; Rebollo-Perdomo, Salomón (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Villaseñor, Gabriel (Instituto Tecnológico de Morelia(México). Departamento de Ciencias Básicas)
In this paper we give a new upper bound for the degree of a class of transversal to infinity invariant algebraic curves for polynomial Kukles systems of arbitrary degree. Moreover, we prove that a quadratic Kukles system having at least one transversal to infinity invariant algebraic curve is integrable.
2016 - 10.14232/ejqtde.2016.1.61
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2016 Núm. 61 (2016) , p. 1-12  
2017-01-23
16:21
28 p, 723.4 KB Periodic orbits of perturbed elliptic oscillators in 6D via averaging theory / Lembarki, Fatima E. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide sufficient conditions on the energy levels to guarantee the existence of periodic orbits for the perturbed elliptic oscillators in 6D using the averaging theory. We give also an analytical estimation of the shape of these periodic orbits parameterized by the energy. [...]
2016 - 10.1007/s10509-016-2930-x
Astrophysics and Space Science. An International Journal of Astronomy, Astrophysics and Space Science, 2016, p. 361-340  
2017-01-23
16:21
9 p, 334.3 KB Hopf periodic orbits for a ratio-dependent predator-prey model with stage structure / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vidal, Claudio (Universidad del Bio Bio(Chile). Departamento de Matemática)
A ratio–dependent predator-prey model with stage structure for prey was investigated in [8]. There the authors mentioned that they were unable to show if such a model admits limit cycles when the unique equilibrium point E ∗ at the positive octant is unstable. [...]
2016 - 10.3934/dcdsb.2016026
Discrete and Continuous Dynamical Systems. Series B, Vol. 21 Núm. 6 (2016) , p. 1859-1867  
2017-01-23
16:21
12 p, 363.9 KB Analytic reducibility of nondegenerate centers: Cherkas systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. We also study the centers for the Cherkas polynomial differential systems x˙ = y, y˙ = P0(x) + P1(x)y + P2(x)y2, where Pi(x) are polynomials of degree n, P0(0) = 0 and P′0(0) < 0. [...]
2016 - 10.14232/ejqtde.2016.1.49
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 49 (2016) , p. 1-10  
2017-01-23
16:21
22 p, 1.1 MB First integrals and phase portraits of planar polynomial differential cubic systems with the maximum number of invariant straight lines / Bujac, Cristina (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vulpe, Nicolae (Academy of Science of Moldova. Institute of Mathematics and Computer Science)
In the article LliVul2006 the family of cubic polynomial differential systems possessing invariant straight lines of total multiplicity 9 was considered and 23 such classes of systems were detected. We recall that 9 invariant straight lines taking into account their multiplicities is the maximum number of straight lines that a cubic polynomial differential systems can have if this number is finite. [...]
2016
Qualitative Theory of Dynamical Systems, Vol. 15 (2016) , p. 327-348