UAB Digital Repository of Documents 31 records found  1 - 10nextend  jump to record: Search took 0.01 seconds. 
1.
6 p, 678.2 KB Periodic orbits of the planar anisotropic generalized Kepler problem / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
Many generalizations of the Kepler problem with homogeneous potential of degree -1/2 have been considered. Here, we deal with the generalized anisotropic Kepler problem with homogeneous potential of degree -1. [...]
2019 - 10.1063/1.5058728
Journal of Mathematical Physics, Vol. 60, Issue 4 (April 2019) , art. 42901  
2.
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 (Universidade de Lisboa. Departamento de Matematica)
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  
3.
25 p, 395.7 KB Symmetric periodic orbits for the collinear charged 3-body problem / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tonon, Durval J. (University of Goiás (Brasil). Institute of Mathematics and Statistics of Federal)
In this paper we study the existence of periodic symmetric orbits of the 3-body problem when each body possess mass and an electric charge. The main technique applied in this study is the continuation method of Poincar\'e.
2017 - 10.1063/1.4974511
Journal of Mathematical Physics, Vol. 58 (2017) , p. 22702  
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.
6 p, 542.7 KB On the periodic solutions of the static, spherically symmetric Einstein-Yang-Mills equations / Buzzi, Claudio Aguinaldo (Universidade Estadual Paulista(Brazil). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We prove that the static, spherically symmetric Einstein-Yang-Mills equations do not have periodic solutions.
2012 - 10.1063/1.4770046
Journal of Mathematical Physics, Vol. 53 (2012) , p. 122703  
6.
19 p, 727.0 KB The 3-dimensional cored and logarithm potencials: Periodic orits / Kulesza, Maite (Universidade Federal Rural de Pernambuco(Brasil). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study analytically families of periodic orbits for the cored and logarithmic Hamiltonians H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (1+x2 +(y2 +z2)/q2)1/2, and H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (log(1+x2 +(y2 + z2)/q2))/2, with 3 degrees of freedom, which are relevant in the analysis of the galactic dynamics. [...]
2014 - 10.1063/1.4901126
Journal of Mathematical Physics, Vol. 55 (2014) , p. 112702  
7.
13 p, 702.2 KB Weierstrass integrability for a class of differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We characterize the differential equations of the form x′ = y, y′ = an(x)yn + an−1(x)yn−1 + · · · + a1(x)y + a0(x), n ≥ 2, an(0) ̸= 0, where aj (x) are meromorphic functions in the variable x for j = 0, . [...]
2014 - 10.1080/14029251.2014.915165
Journal of Nonlinear Mathematical Physics, Vol. 21 Núm. 2 (2014) , p. 294-307  
8.
14 p, 706.0 KB Darboux integrability of 2-dimensional Halmiltonian systems with homogeneous potentials of degree 3 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We provide a characterization of all Hamiltonian systems of the form H = (p21 + p22)/2 + V (q1, q2) where V is a homogenous polynomial of degree 3 which are completely integrable with Darboux first integrals.
2014 - 10.1063/1.4868701
Journal of Mathematical Physics, Vol. 55 (2014) , p. 33507  
9.
25 p, 433.3 KB Liouvillian integrability of gravitating static isothermal fluid spheres / Iacono, Roberto (ENEA-C. R. Casaccia(Italy)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We examine the integrability properties of the Einstein field equations for static, spherically symmetric fluid spheres, complemented with an isothermal equation of state, ρ = np. In this case, Einstein's equations can be reduced to a nonlinear, authonomous second order ODE for m/R (m is the mass inside the radius R) that has been solved analytically only for n = −1 and n = −3, yielding the cosmological solutions by De Sitter and Einstein, respectively, and for n = −5, case for which the solution can be derived from the De Sitter's one using a symmetry of Einstein's equations. [...]
2014 - 10.1063/1.4897213
Journal of Mathematical Physics, Vol. 55 (2014) , p. 102501  
10.
8 p, 280.6 KB The Picard-Fuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system / Fedorov, Yuri (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)
We consider a family of genus 2 hyperelliptic curves of even order and obtain explicitly the systems of 5 linear ordinary differential equations for periods of the corresponding Abelian integrals of first, second, and third kind, as functions of some parameters of the curves. [...]
2014 - 10.1063/1.4868965
Journal of Mathematical Physics, Vol. 55 (2014) , p. 32703  

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