Periodic motion in perturbed elliptic oscillators revisited

M. Corbera, J. Llibre, C. Valls

Producció científica: Contribució a una revistaArticleRecercaAvaluat per experts


© 2016, Springer Science+Business Media Dordrecht. We analytically study the Hamiltonian system in R4 with Hamiltonian H = 1/2(p2x) + p2y + ½ (ω21x2)(ω22y2-εV(x, y) being V(x, y) = − (x2y+ ax3) with a∈ R, where ε is a small parameter and ω1 and ω2 are the unperturbed frequencies of the oscillations along the x and y axis, respectively. Using averaging theory of first and second order we analytically find seven families of periodic solutions in every positive energy level of H when the frequencies are not equal. Four of these seven families are defined for all a∈ R whereas the other three are defined for all a≠ 0. Moreover, we provide the shape of all these families of periodic solutions. These Hamiltonians may represent the central parts of deformed galaxies and thus have been extensively used and studied mainly numerically in order to describe local motion in galaxies near an equilibrium point.
Idioma originalEnglish
Número d’article348
RevistaAstrophysics and Space Science
Estat de la publicacióPublicada - 1 d’oct. 2016


Navegar pels temes de recerca de 'Periodic motion in perturbed elliptic oscillators revisited'. Junts formen un fingerprint únic.

Com citar-ho