The Lissajous transformation. III - Parametric bifurcations

Details The Lissajous transformation. III - Parametric bifurcations The Lissajous transformation. III - Parametric bifurcations

Sep 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991cemda..51..251m&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 51, no. 3, 1991, p. 251-270. Research supported by DARPA.

Mathematics

9

Branching (Physics), Harmonic Oscillation, Lissajous Figures, Nonlinear Equations, Transformations (Mathematics), Equilibrium Equations, Normalizing, Orbital Mechanics, Perturbation Theory

Scientific paper

A parametric family of cubic perturbed 1-1 resonant harmonic oscillators is examined with an aim to understanding the phase flows of the reduced system. Variation of the parameters leads the system through five bifurcations of different types. Some bifurcations are due to passage through cases of discrete symmetry or integrability. A conjecture correlating degenerate equilibria in reduced systems with integrability is modified and reinforced.

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