%0 Journal Article
%A Ibort, A.
%A Martínez Ontalba, Celia
%T Periodic orbits of Hamiltonian systems and symplecticreduction
%D 1996
%@ 0305-4470
%U https://hdl.handle.net/20.500.14352/57627
%X The notion of relative periodic orbits for Hamiltonian systems with symmetry is discussed and a correspondence between periodic orbits of reduced and unreduced Hamiltoniansystems is established. Variational principles with symmetries are studied from the point of view of symplectic reduction of the space of loops, leading to a characterization of reduced periodic orbits by means of the critical subsets of an action functional restricted to a submanifold of the loop space of the unreduced manifold. Finally, as an application, it is shown that if thesymplectic form ! has finite integral rank, then the periodic orbits of a Hamiltonian system on the symplectic manifold .M; !/ admit a variational characterization.
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