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:
2025-02-07
11:43
Limit cycles in a class of planar discontinuous piecewise quadratic differential systems with a non-regular line of discontinuity (I) / He, Dongping (Sichuan University. School of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the limit cycles which bifurcate from the periodic orbits of the quadratic uniform isochronous center ẋ = −y + xy, ẏ = x + y, when this center is perturbed inside the class of all discontinuous piecewise quadratic polynomial differential systems in the plane with two pieces separated by a non-regular line of discontinuity, which is formed by two rays starting from the origin and forming an angle α = π/2. [...]
2025 - 10.1016/j.matcom.2024.10.016
Mathematics and computers in simulation, Vol. 229 (March 2025) , p. 743-757  
2025-02-07
11:43
The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 6 / Dong, Guangfeng (Jinan University. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the topological phase portraits of polynomial differential systems with a uniform isochronous center, whose nonlinear parts are homogeneous polynomials of degree 6. We obtain all the distinct topological phase portraits in the Poincaré disc. [...]
2024 - 10.1007/s10883-024-09703-2
Journal of Dynamical and Control Systems, Vol. 30, Issue 3 (September 2024) , art. 34  
2025-02-07
11:43
On the Global Nilpotent Centers of Cubic Polynomial Hamiltonian Systems / Barreira, Luis (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
A global center for a vector field in the plane is a singular point p having R2 filled of periodic orbits with the exception of the singular point p. Polynomial differential systems of degree 2 have no global centers. [...]
2024 - 10.1007/s12591-022-00606-x
Differential Equations and Dynamical Systems, Vol. 32, Issue 4 (October 2024) , p. 1001-1011  
2025-02-07
11:43
The Global Dynamics of a 3-Dimensional Differential System in ℝ3 via a Darboux Invariant / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
The differential system ẋ = ax − yz, ẏ = −by + xz, ż = −cz + x2, where a, b and c are positive real parameters, has been studied numerically due to the big variety of strange attractors that it can exhibit. [...]
2025 - 10.1007/s10473-025-0204-9
Acta Mathematica Scientia, Vol. 45, Issue 2 (March 2025) , p. 338-346  
2025-02-07
11:43
Limit cycles and chaos in planar hybrid systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Santana, Paulo (Universidade Estadual Paulista "Júlio de Mesquita Filho". Instituto de Biociências, Letras e Ciências Exatas)
In this paper we study the family of planar hybrid differential systems formed by two linear centers and a polynomial reset map of any degree. We study their limit cycles and also provide examples of these hybrid systems exhibiting chaotic dynamics.
2025 - 10.1016/j.cnsns.2024.108382
Communications in nonlinear science and numerical simulation, Vol. 140, Part 1 (January 2025) , art. 108382  
2025-02-07
11:43
Correction to : Limit Cycles in a Class of Planar Discontinuous Piecewise Quadratic Differential Systems with a Non-regular Line of Discontinuity (II) / He, Dongping (Sichuan University. School of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In the original publication, the definition of the angle sector Σ of equation (28) is missing, and it is given in this erratum as follows: (Formula presented. ) The original article has been corrected.
2024 - 10.1007/s00009-024-02730-0
Mediterranean Journal of Mathematics, Vol. 21, Issue 7 (November 2024) , art. 192  
2025-02-07
11:43
16 p, 1.1 MB Cubic planar vector fields with high local cyclicity / Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we present two new one-parameter families of cubic systems exhibiting twelve small-amplitude limit cycles for exceptional parameter values.
2025 - 10.1007/s40863-024-00486-9
São Paulo Journal of Mathematical Sciences, Vol. 19, Issue 1 (June 2025) , art. 4  
2025-02-07
11:43
12 p, 317.0 KB Crossing limit cycles for discontinuous piecewise linear differential centers separated by three parallel straight lines / 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 Matemática) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)
In this paper we study the continuous and discontinuous planar piecewise differential systems formed by four linear centers separated by three parallel straight lines denoted by Σ = {(x,y) ∈ R2 : x = -p, x = 0, x = q, p, q > 0}. [...]
2023 - 10.1007/s12215-022-00766-3
Rendiconti del Circolo Matematico di Palermo, Vol. 72, Issue 3 (April 2023) , p. 1739-1750  
2025-02-07
11:43
28 p, 409.5 KB More limit cycles for complex differential equations with three monomials / Álvarez Torres, María Jesús (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica) ; Coll, Bartomeu (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
In this paper we improve, by almost doubling, the existing lower bound for the number of limit cycles of the family of complex differential equations with three monomials, z˙=Azz¯+Bzz¯+Czz¯, being k,l,m,n,p,q non-negative integers and A,B,C∈C. [...]
2025 - 10.1016/j.jde.2024.10.013
Journal of differential equations, Vol. 416, Part 2 (January 2025) , p. 1071-1098  
2025-02-07
11:43
13 p, 1.1 MB Topological entropy of continuous self-maps on a graph / Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena. Departamento de Matemática Aplicada y Estadística) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Gao, Wei (Yunnan Normal University. School of Information Science and Technology)
Let G be a graph and f be a continuous self-map on G. Using the Lefschetz zeta function of f, we provide a sufficient condition in order that f has positive topological entropy. Moreover, for some classes of graphs we improve this condition making it easier to check.
2019 - 10.1007/s40314-019-0969-3
Computational & Applied Mathematics, Vol. 38, Issue 4 (December 2019) , art. 154