In this paper we study the 3D system with Hamiltonian describing trapped ionic system in the quadrapole field with a superposition of rationally symmetric hexapole and octopole fields for meromorphic integrability. We use the Lyapunov and Ziglin-Morales-Ruiz-Ramis’s classical methods and some new results from the theory of algebraic numbers.
REFERENCES
1.
M.
Benkhali
, J.
Kharbach
, I. E.
Fakkousy
, W.
Chatar
, A.
Rezzouk
, and M.
Ouazzani-Jamil
, “Painleve analysis and integrability of the trapped ionic system
,” Phys. Lett. A
382
, 2515
–2525
(2018
).2.
J.
Morales-Ruiz
, Differential Galois Theory and Non-integrability of Hamiltonian Systems
(Birkhäuser
., 1999
).3.
O.
Christov
and G.
Georgiev
, “Non-integrability of some higher-order painleve equations in the sense of liouville
,” SIGMA 11
045
, 21
(2015
).4.
A.
Baider
and R. C.
Churchill
, “On monodromy groups of second-order fuchsian equations
,” SIAM J. Math. Anal.
21
, 1642
–1652
(1990
).5.
A.
Berger
, “On linear independence of trigonometric numbers, carpathian
,” Carpathian Journal of Mathematics.
34
, 157
–166
(2018
).6.
A.
Lyapunov
, “On certain property of the differential equations of the problem of motion of a heavy rigid body having a fixed point
,” Soobsch. Kharkov Math. Obscht.
2
, 4, 1894, 123
–140
(1954
).7.
E. G. C.
Poole
, Introduction to the Theory of Linear Differential Equations
(Oxford
, At The Clarendon Press
., 1936
).8.
J.
Morales-Ruiz
, J.
Ramis
, and C.
Simó
, “Integrability of hamiltonian systems and differential galois groups of higher variational equations
,” Ann Scient Ec Norm Sup
40
, 845
–884
(2007
).9.
J.
Morales-Ruiz
, “Picard –vessiot theory and integrability
” Journal of Geometry and Physics
87
, 314
–343
(2015
).
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