Journal
CHAOS SOLITONS & FRACTALS
Volume 27, Issue 5, Pages 1220-1228Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2005.04.085
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A canonical transformation is proposed to handle Hamiltonian systems made of the addition or subtraction of three harmonic oscillators in p:q:r resonance. This transformation is an extension of the classical Lissajous transformation for the 1:1 resonance. Our extended Lissajous variables consist of three pairs of action-angle variables, which makes possible the application of perturbation theories without encountering small divisors. A set of functions, related with the Lissajous variables, are found, and are used to describe the phase flow of reduced space after normalization. (c) 2005 Elsevier Ltd. All rights reserved.
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