98-355 Richard Cushman, Sebasti\'an Ferrer, Heinz Han{\ss}mann

Singular Reduction of Axially Symmetric Perturbations of the Isotropic Harmonic Oscillator (516K, PostScript, gzipped and uuencoded) May 21, 98

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Abstract. The normal form of an axially symmetric perturbation of the isotropic harmonic oscillator is invariant under a $2$-torus action and thus integrable in three degrees of freedom. The reduction of this symmetry is performed in detail, showing how the singularities of the reduced phase space determine the distribution of periodic orbits and invariant $2$-tori in the original perturbation. To illustrate these results a particular quartic perturbation is analysed.

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