The Maupertuis principle and integrable systems
arXiv:nlin/0009044
Abstract
We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals of motion, Lax equations, separated variables and action-angles variables. In this review we will discuss namely these induced transformations instead of the various parametric form of the geometric objects.
23 pages, LaTeX, a review for J.Nonlinear Math. Phys