The Existence of Arbitrarily Many Distinct Periodic Orbits in a Two Degree of Freedom Hamiltonian System

Authors

J. J. P. Veerman, Portland State UniversityFollow
Philip Holmes, Cornell University

Sponsor

Partially supported by NSF grant CME 80-17570

Published In

Physica D: Nonlinear Phenomena

Document Type

Citation

Publication Date

1985

Abstract

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.

Rights

Copyright © 1985 Published by Elsevier B.V.

Description

*At the time of publication, Peter Veerman was affiliated with Cornell University.

Locate the Document

https://doi.org/10.1016/0167-2789(85)90177-0

DOI

10.1016/0167-2789(85)90177-0

Persistent Identifier

https://archives.pdx.edu/ds/psu/36008

Citation Details

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.