PERIODIC FIRST INTEGRALS FOR HAMILTONIAN SYSTEMS OF LIE TYPE
2011 ◽
Vol 08
(06)
◽
pp. 1169-1177
◽
Keyword(s):
In this paper, we study the existence problem of periodic first integrals for periodic Hamiltonian systems of Lie type. From a natural ansatz for time-dependent first integrals, we refer their existence to the existence of periodic solutions for a periodic Euler equation on the Lie algebra associated to the original system. Under different criteria based on properties for the Killing form or on exponential properties for the adjoint group, we prove the existence of Poisson algebras of periodic first integrals for the class of Hamiltonian systems considered. We include an application for a nonlinear oscillator having relevance in some modern physics applications.
1984 ◽
Vol 25
(3)
◽
pp. 486-490
◽
1993 ◽
Vol 34
(3)
◽
pp. 997-1006
◽
1986 ◽
Vol 102
(3-4)
◽
pp. 345-363
◽
2010 ◽
Vol 374
(47)
◽
pp. 4746-4748
◽
Keyword(s):
2016 ◽
Vol 32
(5)
◽
pp. 621-632
◽
2008 ◽
pp. 104-116
Keyword(s):