UAB Digital Repository of Documents 10 records found  Search took 0.02 seconds. 
1.
11 p, 310.2 KB Periodic motion in non-axially symmetric galaxies / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)
We apply the averaging theory for proving the existence of twelve families of periodic orbits in a three-dimensional galactic Hamiltonian system.
2019 - 10.1016/j.geomphys.2018.09.023
Journal of geometry and physics, Vol. 140 (June 2019) , p. 1-9  
2.
12 p, 336.3 KB New central configurations of the (n+1)-body problem / Fernandes, Antonio Carlos (Universidade Federal de Itajubá (Brasil). Instituto de Matemática e Computação) ; Garcia, Braulio Augusto (Universidade Federal de Itajubá (Brasil). Instituto de Matemática e Computação) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mello, Luis Fernando (Universidade Federal de Itajubá (Brasil). Instituto de Matemática e Computação)
In this article we study central configurations of the (n+1)-body problem. For the planar (n+1)-body problem we study central configurations performed by ≥2 bodies with equal masses at the vertices of a regular n--gon and one body with null mass. [...]
2018 - 10.1016/j.geomphys.2017.11.003
Journal of geometry and physics, Vol. 124 (Jan. 2018) , p. 199-207  
3.
8 p, 681.1 KB No periodic orbits in the Bianchi models B / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Yu, Jiang (Shanghai Jiao Tong University. Department of Mathematics)
In this paper we prove that the Bianchi models B have no periodic solutions.
2018 - 10.1016/j.geomphys.2018.01.026
Journal of geometry and physics, Vol. 128 (June 2018) , p. 32-37  
4.
14 p, 310.6 KB On the dynamics of a model with coexistence of three attractors: a point, a periodic orbit and a strange attractor / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
For a dynamical system described by a set of autonomous differential equations, an attractor can be either a point, or a periodic orbit, or even a strange attractor. Recently a new chaotic system with only one parameter has been presented where besides a point attractor and a chaotic attractor, it also has a coexisting attractor limit cycle which makes evident the complexity of such a system. [...]
2017 - 10.1007/s11040-017-9240-6
Mathematical Physics, Analysis and Geometry. An International Journal Devoted to the Theory and Applications of Analysis and Geometry to Physics, Vol. 20 Núm. 2 (2017) , p. 1-12  
5.
23 p, 755.7 KB Integrability in nonlinear biomathematical models / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We study the integrability of two biomathematical models described by quadratic polynomial differential systems in the plane. These two models can be divided in six families of differential systems. [...]
2013 - 10.1016/j.geomphys.2013.01.001
Journal of Geometry and Physics, Vol. 66 (2013) , p. 50-70  
6.
17 p, 371.0 KB Darboux integrability of the Lü system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mahdi, Adam (University of North Carolina at Charlotte. Mathematics Department) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We characterize all the values of the parameters of the Lü system, for which it admits a Darboux first integral.
2013 - 10.1016/j.geomphys.2012.10.003
Journal of Geometry and Physics, Vol. 63 (2013) , p. 118-128  
7.
9 p, 295.3 KB Analytic integrability of Bianchi Class A cosmological models with k=1 / Ferragut, Antoni (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)
We complete the study of the analytic integrability of the Class A of Bianchi cosmological models with k = 1, characterizing the analytic first integrals of the Bianchi types VI0 and VIII0.
2012 - 10.1016/j.geomphys.2011.10.022
Journal of Geometry and Physics, Vol. 62 (2012) , p. 381-386  
8.
18 p, 353.0 KB On the periodic orbits of perturbed Hooke Hamiltonian systems with three degrees of freedom / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mello, Luis Fernando (Universidade Federal de Itajubá(Brazil). Instituto de Ciências Exatas)
We study periodic orbits of Hamiltonian differential systems with three degrees of freedom using the averaging theory. We have chosen the classical integrable Hamiltonian system with the Hooke potential and we study periodic orbits which bifurcate from the periodic orbits of the integrable system perturbed with a non–autonomous potential.
2012 - 10.1016/j.geomphys.2011.12.017
Journal of Geometry and Physics, Vol. 62 (2012) , p. 1054-1063  
9.
7 p, 277.9 KB The integrability of the Nose-Hoover equation / Mahdi, Adam (University of North Carolina at Charlotte. Mathematics Department) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
In this work we consider the Nos'e–Hoover equation for a one dimensional oscillator x˙ = −y − xz, y˙ = x, z˙ = α(x2 − 1). It models the interaction of a particle with a heat–bath. We contribute to the understanding of its global dynamics, or more precisely, to the topological structure of its orbits by studying the integrability problem. [...]
2011 - 10.1016/j.geomphys.2011.02.018
Journal of Geometry and Physics, Vol. 61 (2011) , p. 1348-1352  
10.
17 p, 333.3 KB On polynomial integrability of the Euler equations on so(4) / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Yu, Jiang (Shanghai Jiaotong University. Department of Mathematics) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics)
In this paper we prove that the Euler equations on the Lie algebra so(4) with a diagonal quadratic Hamiltonian either satisfy the Manakov condition, or have at most four functionally independent polynomial first integrals. [...]
2015 - 10.1016/j.geomphys.2015.06.001
Journal of Geometry and Physics, Vol. 96 (2015) , p. 36-41  

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