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Periodic orbits of Hamiltonian systems and symplectic reduction

Ibort, A. and Martínez Ontalba, Celia (1996) Periodic orbits of Hamiltonian systems and symplectic reduction. Journal of physics A: Mathematical and general, 29 (3). pp. 675-687. ISSN 0305-4470

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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.

Item Type:Article
Uncontrolled Keywords:relative periodic orbits; Hamiltonian systems; symmetry; variational principles with symmetries; periodic orbits; critical subsets; unreduced manifold
Subjects:Sciences > Mathematics > Differential equations
ID Code:16809

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Last Modified:07 Feb 2014 09:36

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