Integrable systems on the sphere, ellipsoid and hyperboloid

A. V. Tsiganov

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arXiv · 2211.08750

Integrable systems on the sphere, ellipsoid and hyperboloid

A. V. Tsiganov

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Abstract

Affine transformations in Euclidean space generates a correspondence between integrable systems on cotangent bundles to the sphere, ellipsoid and hyperboloid embedded in $R^n$. Using this correspondence and the suitable coupling constant transformations we can get real integrals of motion in the hyperboloid case starting with real integrals of motion in the sphere case. We discuss a few such integrable systems with invariants which are cubic, quartic and sextic polynomials in momenta.

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A. V. Tsiganov. 2022-11-16. Integrable systems on the sphere, ellipsoid and hyperboloid. https://arxiv.org/abs/2211.08750

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