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Continuation of periodic orbits in conservative and Hamiltonian systems. (English) Zbl 1024.37037
Summary: We introduce and justify a computational scheme for the continuation of periodic orbits in systems with one or more first integrals, and in particular in Hamiltonian systems having several independent symmetries. Our method is based on a generalization of the concept of a normal periodic orbit as introduced by J. A. Sepulchre and R. S. MacKay [Nonlinearity 10, 679-713 (1997; Zbl 0905.39004)]. We illustrate the continuation method on some integrable Hamiltonian systems with two degrees of freedom and briefly discuss some further applications.
MSC:
37J35Completely integrable systems, topological structure of phase space, integration methods
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods