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Painlevé analysis and integrability of the trapped ionic system. (English) Zbl 1404.81330

Summary: Integrability in the Painlevé sense of the trapped ionic system in the quadrupole field with superpositions of rotationally symmetric hexapole and octopole fields is studied. Five integrable cases of the system are reported. First integrals of the planar motion are founded. Confirming three-dimensional integrability of the equations of motion, the third explicit integrals of motion are constructed directly for each case. We carry out a numerical study to observe the regularity and chaotic regions via the Poincaré surface of sections, and corroborate the analytical results.

MSC:

81V55 Molecular physics
81R12 Groups and algebras in quantum theory and relations with integrable systems
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
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