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Zbl 1024.37037
Muñoz-Almaraz, F.J.; Freire, E.; Galán, J.; Doedel, E.; Vanderbauwhede, A.
Continuation of periodic orbits in conservative and Hamiltonian systems.
(English)
[J] Physica D 181, No.1-2, 1-38 (2003). ISSN 0167-2789

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 {\it J. A. Sepulchre} and {\it 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 2000:
*37J35 Completely integrable systems, etc.
37J45 Periodic, homoclinic and heteroclinic orbits, etc.

Keywords: computational scheme; first integrals; integrable systems

Citations: Zbl 0905.39004

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