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

Latest additions:
2016-05-06
10:59
25 p, 696.1 KB Darboux integrability and Algebraic limit cycles for a class of polynomial differential Systems / Cao, Jinlong ; Llibre, Jaume ; Zhang, Xiang
This paper deals with the existence of Darboux first integrals for the planar polynomial differential systems x˙ = λx − y + Pn+1 (x, y) + xF2n (x, y), y˙ = x + λy + Qn+1 (x, y)+yF2n (x, y), where Pi (x, y), Qi (x, y) and Fi (x, y) are homogeneous polynomials of degree i. [...]
2014 - 10.1007/s11425-014-4772-8
Science China Mathematics, Vol. 57 Núm. 4 (2014) , p. 775-794  
2016-05-06
10:59
19 p, 1.5 MB Sierpinski curve Julia sets for quadratic rational maps / Devaney, Robert L. (Boston University. Department of Mathematics) ; Fagella, Núria (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ; Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i matemàtiques) ; Jarque, Xavier (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpi ́nski curve.
2014 - 10.5186/aasfm.2014.3903
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica, Vol. 39 (2014) , p. 3-22  
2016-05-06
10:59
5 p, 607.4 KB On the analytic integrability of the 5-dimensional Lorenz system for the gravitiy-wave activity / Llibre, Jaume ; Saghin, Radu ; Zhang, Xiang
2014 - 10.1090/S0002-9939-2013-11773-9
Proceedings of the American Mathematical Society, Vol. 142 Núm. 2 (2014) , p. 531-537  
2016-05-06
10:59
17 p, 657.2 KB Limit cycles bifurcating from a non-isolated zero-Hopf equilibrium of three-dimensional differential systems / Llibre, Jaume ; Xiao, Dongmei
2014 - 10.1090/S0002-9939-2014-11923-X
Proceedings of the American Mathematical Society, Vol. 142 Núm. 6 (2014) , p. 2047-2062  
2016-05-06
10:59
10 p, 766.6 KB Algebraic invariant curves and first integrals for Riccati polynomial differential systems / Llibre, Jaume ; Valls, Clàudia
2014 - 10.1090/S0002-9939-2014-12085-5
Proceedings of the American Mathematical Society, Vol. 142 Núm. 10 (2014) , p. 3533-3543  
2016-05-06
10:59
11 p, 310.2 KB On the global asymptotic stability of difference equations satisfying a Markus-Yamabe condition / Cimà, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We prove a global asymptotic stability result for maps coming from n-th order difference equation and satisfying a Markus-Yamabe type condition. We also show that this result is sharp.
2014 - 10.5565/PUBLMAT_Extra14_09
Publicacions Matematiques, Vol. Extra (2014) , p. 167-178  
2016-05-06
10:59
9 p, 570.0 KB On the periodic orbit bifurcating from a Hopf bifurcation in systems with two slow and one fast variables / García, Isaac A. ; Llibre, Jaume ; Maza, Susanna
2014 - 10.1016/j.amc.2013.12.184
Applied Mathematics and Computation, Vol. 232 (2014) , p. 84-90  
2016-05-06
10:59
52 p, 1.0 MB Inverse Approach in Ordinary Differential Equations: Applications to Lagrangian and Hamiltonian Mechanics / Llibre, Jaume ; Ramírez, Rafael Orlando ; Sadovskaia, Natalia
2014 - 10.1007/s10884-014-9390-1
Journal of Dynamics and Differential Equations, Vol. 26 (2014) , p. 529-581  
2016-05-06
10:59
10 p, 718.0 KB On the limit cycles of the Floquet differential equations / Llibre, Jaume ; Rodrigues, Ana
2014 - 10.3934/dcdsb.2014.19.1129
Discrete and Continuous Dynamical Systems. Series B, Vol. 19 Núm. 4 (2014) , p. 1129-1136  
2016-05-06
10:59
11 p, 650.3 KB Global dynamics of the Kummer-Schwarz differential equation / Llibre, Jaume ; Vidal, Claudio
2014 - 10.1007/s00009-013-0299-4
Mediterranean Journal of Mathematics, Vol. 11 (2014) , p. 477-486