The Kepler canonical transformations of the extended phase space (Q1577158)

The author considers compositions of transformations of the time variable and canonical transformations of the other coordinates. If the transformation maps a completely integrable system into another completely integrable system, then the transformations of the whole machinery developed for integrable systems is induced: that of the integrals of the motion, Lax pairs, and that of the corresponding spectral curves and R-matrices. The author studies such transformations for several important cases of integrable systems.