Bäcklund transformations for the nonholonomic Veselova system

Abstract

We present auto and hetero Bäcklund transformations of the nonholonomic Veselova system using standard divisor arithmetic on the hyperelliptic curve of genus two. As a by-product one gets two natural integrable systems on the cotangent bundle to the unit two-dimensional sphere whose additional integrals of motion are polynomials in the momenta of fourth order.

16 pages, 3 figures, LaTeX with AMSfonts

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• Duffing oscillator and elliptic curve cryptography
• Equivalent Integrable Metrics on the Sphere with Quartic Invariants