2010/08/31 by A. Sergyeyev · 1 citation
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.MP
paper · pdf · doi:10.1016/j.physleta.2012.04.055
published as Phys. Lett. A 376 (2012), no. 28-29, 2015-2022 · 12 pages, LaTeX
arxiv created 2012/04/28 · arxiv updated 2017/09/29
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.