Integrable systems on the sphere, ellipsoid and hyperboloid

2022/11/16 by Tsiganov, A. V. · 1 citation
#Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2211.08750

Abstract

Affine transformations in Euclidean space generates a correspondence between integrable systems on cotangent bundles to the sphere, ellipsoid and hyperboloid embedded in Rⁿ. 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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