The Existence of Arbitrarily Many Distinct Periodic Orbits in a Two Degree of Freedom Hamiltonian System
Partially supported by NSF grant CME 80-17570
Physica D: Nonlinear Phenomena
Melnikov's method is used to prove the existence of arbitrarily many elliptic and hyperbolic periodic orbits in the neighborhood of an elliptic orbit of a two degree of freedom Hamiltonian system which is ‘almost integrable’. The existence of such orbits precludes the existence of analytic second integrals of a certain type. The methods used permit a detailed analysis of the way in which resonant tori break up between the KAM irrational tori which are preserved for weak coupling of two independent nonlinear oscillators.
Copyright © 1985 Published by Elsevier B.V.
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Veerman, P., & Holmes, P. (1985). The existence of arbitrarily many distinct periodic orbits in a two degree of freedom Hamiltonian system. Physica D: Nonlinear Phenomena, 14(2), 177-192.