UAB Digital Repository of Documents 5 records found  Search took 0.04 seconds. 
1.
28 p, 723.4 KB Periodic orbits of perturbed elliptic oscillators in 6D via averaging theory / Lembarki, Fatima Ezzahra (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide sufficient conditions on the energy levels to guarantee the existence of periodic orbits for the perturbed elliptic oscillators in 6D using the averaging theory. We give also an analytical estimation of the shape of these periodic orbits parameterized by the energy. [...]
2016 - 10.1007/s10509-016-2930-x
Astrophysics and Space Science. An International Journal of Astronomy, Astrophysics and Space Science, 2016, p. 361-340  
2.
23 p, 689.0 KB Periodic motion in perturbed elliptic oscillators revisited / Corbera Subirana, Montserrat (Universitat de Vic. Departament de Tecnologies Digitals i de la Informació) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We analytically study the Hamiltonian system in R^4 with Hamiltonian H= 12 (p_x^2 p_y^2) 12 (_1^2 x^2 _2^2 y^2)- V_1(x,y) being (a) V_1(x,y)=-(xy^2 ax^3) and (b) V_1(x,y)=-(x^2y ax^3) with aR, where is a small parameter and _1 and _2 are the unperturbed frequencies of the oscillations along the x and y axis, respectively. [...]
2016 - 10.1007/s10509-016-2927-5
Astrophysics and Space Science. An International Journal of Astronomy, Astrophysics and Space Science, Vol. 361:348 (2016) , p. 1-8  
3.
8 p, 626.3 KB Periodic orbits and non-integrability of Armbruster-Guckenheimer-Kim potential / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Roberto, Lucy Any (Universidade Estadual Júlio de Mesquita(Brasil). Departamento de Matemática)
In this paper we study the periodic orbits of the Hamiltonian system with the Armburster-Guckenheimer-Kim potential and its non-integrability in the sense of Liouville–Arnold.
2013 - 10.1007/s10509-012-1210-7
Astrophysics and Space Science. An International Journal of Astronomy, Astrophysics and Space Science, Vol. 343 Núm. 1 (2013) , p. 69-74  
4.
9 p, 320.5 KB Periodic orbits for a class of galactic potentials / Alfaro Aguilar, Felipe (UACM(México). Academia de Matemáticas) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pérez-Chavela, Ernesto (UAM-Iztapalapa(México). Departamento de Matemáticas)
In this work, applying general results from averaging theory, we find periodic orbits for a class of Hamiltonian systems H whose potential models the motion of elliptic galaxies. Using the above periodic orbits on the energy level H = h we provide information about the non-integrability, in the sense of Liouville–Arnold, of the respective Hamiltonian system generated by H.
2013 - 10.1007/s10509-012-1318-9
Astrophysics and Space Science. An International Journal of Astronomy, Astrophysics and Space Science, Vol. 344 Núm. 1 (2013) , p. 39-44  
5.
10 p, 710.0 KB Periodic orbits of the generalized Friedmann-Robertson-Walker Hamiltonian systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba(Algeria). Department of Mathematics)
We provide sufficient conditions for the existence of periodic solutions of the second order Hamiltonian system −x′′ − λx = εV ′x (t, x), where ε is a small parameter, x ∈ R and V (t, x) is 2π-periodic in t. [...]
2013 - 10.1007/s10509-012-1314-0
Astrophysics and Space Science. An International Journal of Astronomy, Astrophysics and Space Science, Vol. 344 Núm. 1 (2013) , p. 45-50  

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