Coupling constant metamorphosis as an integrability-preserving transformation for general finite-dimensional dynamical systems and ODEs

Abstract

In the present paper we extend the multiparameter coupling constant metamorphosis, also known as the generalized Stäckel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This transform interchanges the values of integrals of motion with the parameters these integrals depend on but leaves the phase space coordinates intact. Sufficient conditions under which the transformation in question preserves integrability and a simple formula relating the solutions of the original system to those of the transformed one are given.

12 pages, LaTeX

References in corpus (3)

• Generalized Stäckel Transform and Reciprocal Transformations for Finite-Dimensional Integrable Systems
• Differential Galois theory and Integrability
• Ordinary differential equations which linearize on differentiation

Cited by in corpus (5)

• On reciprocal equivalence of Stäckel systems
• Null lifts and projective dynamics
• Deforming Lie algebras to Frobenius integrable non-autonomous Hamiltonian systems
• Integrable quantum Stäckel systems
• Integrability of non-homogeneous Hamiltonian systems with gyroscopic coupling