2026-06-30T03:13:41Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/576272023-08-25T11:30:43Zcom_20.500.14352_14col_20.500.14352_15

Periodic orbits of Hamiltonian systems and symplectic reduction Ibort, A. Martínez Ontalba, Celia The notion of relative periodic orbits for Hamiltonian systems with symmetry is discussed and a correspondence between periodic orbits of reduced and unreduced Hamiltonian systems 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 the symplectic form ! has finite integral rank, then the periodic orbits of a Hamiltonian system on the symplectic manifold .M; !/ admit a variational characterization. 2023-06-20T17:00:55Z 2023-06-20T17:00:55Z 2023-06-20T17:00:55Z 1996 journal article https://hdl.handle.net/20.500.14352/57627 0305-4470 10.1088/0305-4470/29/3/018 eng PB92/0197 CRG 940195 AP92 (CMO). restricted access IOP Publishing