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:
2017-12-07
16:24
14 p, 313.9 KB On extended chebyshev systems with positive accuracy / Novaes, Douglas D. (Universidade Estadual de Campinas (Brasil). Departamento de Matemática) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
A classical necessary condition for an ordered set of n+1 functions F to be an ECT-system in a closed interval is that all the Wronskians do not vanish. With this condition all the elements of Span(F) have at most n zeros taking into account the multiplicity. [...]
2017 - 10.1016/j.jmaa.2016.10.076
Journal of Mathematical Analysis and Applications, Vol. 448 Núm. 1 (April 2017) , p. 171-186  
2017-12-07
15:53
15 p, 853.0 KB Centers for the Kukles homogeneous systems with even degree / Giné, Jaume (Universitat de Lleida. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
2017
Journal of Applied Analysis and Computation, Vol. 7 Núm. 4 (2017) , p. 1534-1548  
2017-12-07
15:21
9 p, 590.4 KB On the periodic solutions of the 5–dimensional Lorenz equation modeling coupled Rosby waves and gravity waves / de Carvalho, Tiago (Universidade Estadual Paulista (Brasil). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
2017 - 10.1142/S0218127417500900
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 27 Núm. 6 (Junio 2017)  
2017-11-28
08:46
9 p, 291.9 KB On the global dynamics of a finance model / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia
Recently several works have studied the following model of finance \[ x= z (y-a) x, y= 1-b y -x^2, z= -x -c z, \] where a, b and c are positive real parameters. We study the global dynamics of this polynomial differential system, and in particular for a one--dimensional parametric subfamily we show that there is an equilibrium point which is a global attractor.
2018 - 10.1016/j.chaos.2017.10.026
Chaos, Solitons and Fractals, Vol. 106 (2018) , p. 1-4  
2017-11-28
08:46
22 p, 333.2 KB Bifurcation of 2-periodic orbits from non-hyperbolic fixed points / Cimà, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mañosa Fernández, Víctor (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
We introduce the concept of 2-cyclicity for families of one-dimensional maps with a non-hyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful in order to study the number of 2-periodic orbits that can bifurcate from the fixed point. [...]
2018 - 10.1016/j.jmaa.2017.08.029
Journal of Mathematical Analysis and Applications, Vol. 457 (2018) , p. 568-584  
2017-11-28
08:46
21 p, 834.1 KB Centers for generalized quintic polynominal differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia
2017 - 10.1216/RMJ-2017-47-4-1097
Rocky Mountain Journal of Mathematics, Vol. 47 Núm. 4 (2017) , p. 1097-1120  
2017-11-28
08:46
235 p, 1.6 MB Estudi de la dinàmica d'algunes aplicacions al pla / Llorens, Mireia (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Gasull i Embid, Armengol, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mañosa Fernández, Víctor, dir. (Universitat Politècnica de Catalunya. Departament de Matemàtiques) ; Universitat Autònoma de Barcelona. Grup de Sistemes Dinàmics
Bellaterra 2017  
2017-11-28
08:46
12 p, 699.2 KB Proper rational and analytic first integrals for asymmetric 3-dimensional Lotka-Volterra systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia
We go beyond in the study of the integrability of the classical model of competition between three species studied by May and Leonard [19], by considering a more realistic asymmetric model. Our results show that there are no global analytic first integrals and we provide all proper rational first integrals of this extended model by classifying its invariant algebraic surfaces.
2017 - 10.1080/14029251.2017.1341701
Journal of Nonlinear Mathematical Physics, Vol. 24 Núm. 3 (2017) , p. 393-404  
2017-11-28
08:46
3 p, 583.8 KB Erratum to: A Network Epidemic Model with Preventive Rewiring: Comparative Analysis of the Initial Phase / Britton, Tom (Stockholm University. Department of Mathematics) ; Juher, David (Universitat de Girona. Departament d’Informàtica, Matemàtica Aplicada i Estadística) ; Saldaña, Joan (Universitat de Girona. Departament d’Informàtica, Matemàtica Aplicada i Estadística)
2017 - 10.1007/s11538-017-0295-0
Bulletin of Mathematical Biology, Vol. 79 (2017) , p. 1687-1689  
2017-11-28
08:46
31 p, 6.8 MB Numerical study of the geometry of the phase space of the augmented Hill three-body problem / Farrés, Ariadna (Universitat de Barcelona. Institut de Matemàtiques) ; Jorba, Àngel (Universitat de Barcelona. Departament de Matemàtiques i Informàtica) ; Mondelo González, José María (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The Augmented Hill Three-Body problem is an extension of the classical Hill problem that, among other applications, has been used to model the motion of a solar sail around an asteroid. This model is a 3 degrees of freedom (3DoF) Hamiltonian system that depends on four parameters. [...]
2017 - 10.1007/s10569-017-9762-z
Celestial Mechanics & Dynamical Astronomy. An International Journal of Space Dynamics, 2017