GSD (Grupo de Sistemas Dinámicos)

Los sistemas dinámicos son, y siempre han sido, una de las principales líneas de investigación en Matemáticas. Es de interés de todas las civilizaciones humanas el comprender cuestiones importantes, como el movimiento de los planetas, la evolución de las poblaciones, o el estudio de la dinámica en sistemas deterministas, de modo que los sistemas dinámicos se han convertido en un objetivo importante de estudio. Después de muchos años de evolución, el área de los sistemas dinámicos ha sufrido varias transformaciones y ha desarrollado distintas ramas que han permitido responder preguntas de diversa índole.

Las líneas principales de investigación del Grupo de Sistemas Dinámicos de la UAB (GSD-UAB) son: Mecánica celeste, Dinámica compleja, Sistemas Dinámicos discretos y Teoría cualitativa de ecuaciones diferenciales.

Los miembros de nuestro grupo trabajan principalmente en las universidades catalanas (UAB, UB, UdG, UPC, URV, UVic), aunque algunos de nuestros investigadores trabajan en otras universidades de España y del extranjero. El GSD-UAB colabora asiduamente con varios grupos de investigación nacionales e internacionales.

Página web: http://www.gsd.uab.cat

Estadísticas de uso Los más consultados
Últimas adquisiciones:
2018-11-12
13:11
7 p, 289.4 KB Limit cycles of a second-order differential equation / Chen, Ting (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide an upper for the maximum number of limit cycles bifurcating from the periodic solutions of x=0, when we perturb this system as follows \ (1 ^m )Q(x,y) x=0, \] where >0 is a small parameter, m is an arbitrary non-negative integer, Q(x,y) is a polynomial of degree n and =(y/x). [...]
2019 - 10.1016/j.aml.2018.08.015
Applied mathematics letters, Vol. 88 (2019) , p. 111-117  
2018-11-12
13:11
15 p, 328.9 KB Subseries and signed series / Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
For any positive decreasing to zero sequence a_n such that Ʃa_n diverges we consider the related series Ʃk_na_n and Ʃj_na_n. Here, k_n and j_n are real sequences such that Ʃk_nє{0,1} and j_nє{-1,1}. [...]
2019 - 10.3934/cpaa.2019024
Communications on pure & applied analysis, Vol. 18, issue 1 (Jan. 2019) , p. 479-492  
2018-11-12
13:11
25 p, 4.7 MB Convergence regions for the Chebyshev--Halley family / Campos, Beatriz (Institut Universitari de Matemàtiques i Aplicacions de Castelló) ; Canela, Jordi (Institut Universitari de Matemàtiques i Aplicacions de Castelló) ; Vindel, Pura (Institut Universitari de Matemàtiques i Aplicacions de Castelló)
In this paper, we study the dynamical behaviour of the Chebyshev--Halley family applied on a family of degree n polynomials. For n=2 we bound the set of parameters for which the iterative methods have convergence regions which do not correspond to the basins of attraction of the roots. [...]
2018 - 10.1016/j.cnsns.2017.08.024
Communications in nonlinear science and numerical simulation, Vol. 56 (March 2018) , p. 508-525  
2018-11-12
13:11
23 p, 5.9 MB Rational maps with Fatou components of arbitrarily large connectivity / Canela Sánchez, Jordi (Université Paul Sabatier. Institut de Mathématiques de Toulouse)
We study the family of singular perturbations of Blaschke products B_a,(z)=z^3-a1- ^2. We analyse how the connectivity of the Fatou components varies as we move continuously the parameter . We prove that all possible escaping configurations of the critical point c_-(a,) take place within the parameter space. [...]
2018 - 10.1016/j.jmaa.2018.01.061
Journal of mathematical analysis and applications, Vol. 462, issue 1 (June 2018) , p. 35-56  
2018-11-12
13:11
13 p, 271.6 KB Periodic orbits bifurcating from a nonisolated zero-Hopf equilibrium of three-dimensional differential systems revisited / Cândido, Murilo R. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we study the periodic solutions bifurcating from a nonisolated zero–Hopf equilib- rium in a polynomial differential system of degree two in R³. More specifically, we use recent results of averaging theory to improve the conditions for the existence of one or two periodic solutions bifurcating from such a zero–Hopf equilibrium. [...]
2018 - 10.1142/S021812741850058X
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 28, no. 5 (2018) , art. 1850058  
2018-11-12
13:11
29 p, 5.8 MB Zero--Hopf bifurcations in 3-dimensional differential systems with no equilibria / Cândido, Murilo R. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We use averaging theory for studying the Hopf and zero--Hopf bifurcations in some chaotic differential systems. These differential systems have a chaotic attractor and no equilibria. Numerically we show the relation between the existence of the periodic solutions studied in these systems and their chaotic attractors.
2018 - 10.1016/j.matcom.2018.03.008
Mathematics and computers in simulation, Vol. 151 (Sep. 2018) , p. 54-76  
2018-11-12
13:11
28 p, 448.6 KB Differential Galois theory and non-integrability of planar polynomial vector fields / Acosta-Humánez, Primitivo B. (Universidad Simón Bolívar(Colombia). Facultad de Ciencias Básicas y Biomédicas) ; Tomás Lázao, J. (Universitat Politècnica de Catalunya. Departament de Matemàtiques) ; Morales-Ruiz, Juan J. (Universidad Politécnica de Madrid. Departamento de Matemática Aplicada) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica)
We study a necessary condition for the integrability of the polynomials vector fields in the plane by means of the differential Galois Theory. More concretely, by means of the variational equations around a particular solution it is obtained a necessary condition for the existence of a rational first integral. [...]
2018 - 10.1016/j.jde.2018.02.016
Journal of differential equations, Vol. 264, issue 12 (June 2018) , p. 7183-7212  
2018-11-12
13:11
15 p, 876.8 KB Tuning the overlap and the cross-layer correlations in two-layer networks : application to an SIR model with awareness dissemination / Juher, David (Universitat de Girona. Departament d’Informàtica, Matemàtica Aplicada i Estadística) ; Saldaña, Joan (Universitat de Girona. Departament d’Informàtica, Matemàtica Aplicada i Estadística)
We study the properties of the potential overlap between two networks A,B sharing the same set of N nodes (a two-layer network) whose respective degree distributions p_A(k), p_B(k) are given. Defining the overlap coefficient as the Jaccard index, we prove that is very close to 0 when A and B are random and independently generated. [...]
2018 - 10.1103/PhysRevE.97.032303
Physical review E, Vol. 97, issue 3 (March 2018) , art. 32303  
2018-11-12
13:11
22 p, 627.8 KB Periodic points of a Landen transformation / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llorens, Mireia (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mañosa, Víctor (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
We prove the existence of 3-periodic orbits in a dynamical system associated to a Landen transformation previously studied by Boros, Chamberland and Moll, disproving a conjecture on the dynamics of this planar map introduced by the latter author. [...]
2018 - 10.1016/j.cnsns.2018.04.020
Communications in nonlinear science and numerical simulation, Vol. 64 (Nov. 2018) , p. 232-245  
2018-11-12
13:11
10 p, 362.5 KB A proof of Bertrand’s theorem using the theory of isochronous potentials / Ortega, Rafael (Universidad de Granada. Departamento de Matemática Aplicada) ; Rojas, David (Universidad de Granada. Departamento de Matemática Aplicada)
We give an alternative proof for the celebrated Bertrand’s theorem as a corollary of the isochronicity of a certain family of centers.
2018 - 10.1007/s10884-018-9676-9
Journal of dynamics and differential equations, Published online May 2018