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.
Keywords:
nonholonomic dynamical system, bi-Hamiltonian geometry, Bäcklund transformations
Citation:
Tsiganov A. V., Bäcklund Transformations for the Nonholonomic Veselova System, Regular and Chaotic Dynamics,
2017, Volume 22, Number 2,
pp. 163-179