GSD (Grupo de sistemas dinámicos) - Depósito Digital de Documentos de la UAB

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

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2024-11-28
20:33

37 p, 834.6 KB

Periodic Orbits In The Zero-Hopf Bifurcations Of 3-Dimensional Kolmogorov Systems Of Degree 3 / Bouaziz, Chamseddine (University of Annaba. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Djedid, Djamila (University of Annaba. Department of Mathematics) ; Makhlouf, Amar (University of Annaba. Department of Mathematics)
We study the zero Hopf bifurcation of 3-dimensional Kolmogorov systems using first-order averaging theory. We find that one or two limit cycles can bifurcate from the singular point.
2024
Applied Mathematics E-Notes, Vol. 24 (2024) , p. 237-273

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2024-11-28
19:36

11 p, 835.1 KB

The Dynamics of the Ladder System / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We consider the n-dimensional ladder system, that is the homogeneous differential systems of the form [Formula presented] introduced by Imai and Hirata for studying the integrability of a new class of Lotka-Volterra systems. [...]
2024 - DOI (Digital Object Identifier)

10.7566/JPSJ.93.014001
Journal of the Physical Society of Japan, Vol. 93, Issue 1 (January 2024) , art. 014001

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2024-11-28
19:11

6 p, 252.5 KB

Periodic orbits of continuous-discontinuous piecewise differential systems with four pieces separated by the curve xy = 0 and formed by linear Hamiltonian systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Salhi, Tayeb (University Mohamed El Bachir El Ibrahimi. Department of Mathematics)
In recent years there has been a significant interest in studying the piecewise differential systems, mainly due to their wide range of applications in modeling natural phenomena. To understand the dynamics of such systems in the plane is a significant challenge, particularly when we want to study their periodic orbits and, more specifically, their limit cycles. [...]
2024
Dynamics of continuous, discrete and impulsive systems, Vol. 31, Issue 4 (2024) , p. 279-286

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2024-11-25
11:58

5 p, 612.3 KB

On my eight articles with the Professor Jorge Sotomayor / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this note I summarize the eight articles that I wrote with the Professor Jorge Sotomayor and the consequences of some these articles.
2024 - DOI (Digital Object Identifier)

10.1007/s40863-024-00434-7
São Paulo Journal of Mathematical Sciences, (2024)

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2024-11-25
11:58

14 p, 416.7 KB

Limit Cycles for a Class of Continuous-Discontinuous Piecewise Differential Systems / Ghermoul, Bilal (University Mohamed El Bachir El-Ibrahimi. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
During this century, an increasing interest appeared in studying the planar piecewise differential systems. This is due to their numerous applications for modelling many natural phenomena. For understanding the dynamics of the planar differential systems we must control the existence or non-existence of periodic orbits and limit cycles. [...]
2024 - DOI (Digital Object Identifier)

10.12150/jnma.2024.669
Journal of Nonlinear Modeling and Analysis, Vol. 6 , Issue 3 (September 2024) , p. 669-682

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2024-11-25
11:48

The Jerk Dynamics of Lorenz Model / Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Aix Marseille University. Université de Toulon) ; Meucci, Riccardo (Consiglio Nazionale Delle Ricerche. Istituto Nazionale Di Ottica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Sprott, Julien Clinton (University of Wisconsin)
The Lorenz model is widely considered as the first dynamical system exhibiting a chaotic attractor, the shape of which is the famous butterfly. This similarity led Lorenz to name the sensitivity to initial conditions inherent to such chaotic systems the butterfly effect, making its model a paradigm of chaos. [...]
Springer Cham, 2024 (NODYCON Conference Proceedings Series) - DOI (Digital Object Identifier)

10.1007/978-3-031-50635-2_12
Advances in Nonlinear Dynamics, Volume III. Proceedings of the Third International Nonlinear Dynamics Conference (NODYCON 2023), 2024, p. 121-129

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2024-11-25
11:43

16 p, 775.0 KB

Flexibility of Entropies for Piecewise Expanding Unimodal Maps / Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Misiurewicz, Michal (Indiana University-Purdue University Indianapolis. Department of Mathematical Sciences) ; Pérez, Rodrigo A. (Indiana University-Purdue University Indianapolis. Department of Mathematical Sciences)
We investigate the flexibility of the entropy (topological and metric) for the class of piecewise expanding unimodal maps. We show that the only restrictions for the values of the topological and metric entropies in this class are that both are positive, the topological entropy is at most log 2, and the metric entropy is not larger than the topological entropy. [...]
Cambridge University Press, 2024 - DOI (Digital Object Identifier)

10.1017/9781009278898.003
A Vision for Dynamics in the 21st Century: The Legacy of Anatole Katok, (February 2024) , p. 48-66

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2024-11-14
12:11

New families of global cubic centers / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Serantola, Leonardo P. (Universidade Estadual Paulista "Júlio de Mesquita Filho". Instituto de Biociências, Letras e Ciências Exatas)
An equilibrium point p of a differential system in the plane R2 is a center if there exists a neighbourhood U of p such that U\{p} is filled with periodic orbits. A difficult classical problem in the qualitative theory of differential systems in the plane R2 is the problem of distinguishing between a focus and a center. [...]
2024 - DOI (Digital Object Identifier)

10.1007/s40863-024-00411-0
São Paulo Journal of Mathematical Sciences, (March 2024)

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2024-11-14
12:11

49 p, 575.0 KB

Invariant manifolds of maps and vector fields with nilpotent parabolic tori / Cufí Cabré, Clara (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Fontich, Ernest 1955- (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
We consider analytic maps and vector fields defined in R2 × Td, having a d-dimensional invariant torus T. The map (resp. vector field) restricted to T defines a rotation of Diophantine frequency vector ω ∈ Rd, and its derivative restricted to transversal directions to T does not diagonalize. [...]
2024 - DOI (Digital Object Identifier)

10.1016/j.jde.2024.03.030
Journal of differential equations, Vol. 396 (July 2024) , p. 314-362

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2024-11-14
12:11

Periods of Self-Maps on S2 Via their Homology / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
As usual, we denote a 2-dimensional sphere by S2. We study the periods of periodic orbits of the maps f : S2 → S2 that are either continuous or C with all their periodic orbits being hyperbolic, or transversal, or holomorphic, or transversal holomorphic. [...]
2024 - DOI (Digital Object Identifier)

10.1007/s11253-024-02308-9
Ukrainian Mathematical Journal, Vol. 76, Issue 1 (June 2024) , p. 76-79

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