TOPOLOGY AND PERIODIC ORBITS OF RING-SHAPED POTENTIALS AS A GENERALIZED 4-D ISOTROPIC OSCILLATOR
2010 ◽
Vol 20
(09)
◽
pp. 2809-2821
Keyword(s):
In this work we study a generalized integrable biparametric family of 4-D isotropic oscillators. This family allows to treat, in a unified way, oscillators defined by the potentials given by Hartmann and Quesne and other ring-shaped systems. Using the Liouville–Arnold theorem and the analysis of the momentum map in its critical points, we obtain a complete topological classification of the different invariant sets of the phase flow of this problem. By this topological study and the calculation of the action-angle variables we obtain the full classification of periodic and quasiperiodic orbits for this system.
2018 ◽
Vol 32
(15)
◽
pp. 1850155
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2018 ◽
Vol 123
(2)
◽
pp. 20005
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2018 ◽
Vol 32
(21)
◽
pp. 1850227
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2010 ◽
Vol 16
(5-6)
◽
pp. 411-423
◽
1989 ◽
Vol 6
(2)
◽
pp. 291-330
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