Canonical transformations of the extended phase space, Toda lattices and Stackel family of integrable systems

Abstract

We consider compositions of the transformations of the time variable and canonical transformations of the other coordinates, which map completely integrable system into other completely integrable system. Change of the time gives rise to transformations of the integrals of motion and the Lax pairs, transformations of the corresponding spectral curves and R-matrices. As an example, we consider canonical transformations of the extended phase space for the Toda lattices and the Stackel systems.

LaTeX2e + Amssymb, 22pp

References in corpus (4)

• Duality between integrable Stackel systems
• Invariants at fixed and arbitrary energy. A unified geometric approach
• The Lax pairs for the Holt system
• Canonical transformations of the time for the Toda lattice and the Holt system

Cited by in corpus (15)

• Hamiltonian dynamics on the symplectic extended phase space for autonomous and non-autonomous systems
• On the Drach superintegrable systems
• The Maupertuis principle and canonical transformations of the extended phase space
• Generalized Stäckel Transform and Reciprocal Transformations for Finite-Dimensional Integrable Systems
• Third-order superintegrable systems separable in parabolic coordinates
• On reciprocal equivalence of Stäckel systems
• One invariant measure and different Poisson brackets for two nonholonomic systems
• Nonautonomous Hamiltonian Systems and Morales-Ramis Theory I. The Case $\ddot{x}=f(x,t)$
• Extended Hamilton-Lagrange formalism and its application to Feynman's path integral for relativistic quantum physics
• Canonical transformations of the time for the Toda lattice and the Holt system
• Non-Integrability of a weakly integrable Hamiltonian system
• Transformation of the Stackel matrices preserving superintegrability
• Simple non-Hamiltonian systems with an invariant measure
• Reciprocal transformations for Stackel-related Liouville integrable systems
• Stäckel transform of Lax equations