Ibort, A.Martínez Ontalba, Celia2023-06-202023-06-2019960305-447010.1088/0305-4470/29/3/018https://hdl.handle.net/20.500.14352/57627The 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.engjournal articlehttp://iopscience.iop.org/0305-4470/29/3/018http://www.iop.orgrestricted access517.9relative periodic orbitsHamiltonian systemssymmetryvariational principles with symmetriesperiodic orbitscritical subsetsunreduced manifoldEcuaciones diferenciales1202.07 Ecuaciones en Diferencias