Sergyeyev A. Coupling constant metamorphosis, integrability and all that, talk at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic (abstract)
Speaker: Artur Sergyeyev
Title: Coupling constant metamorphosis, integrability and all that
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. The details can be found in the paper A. Sergyeyev, Phys. Lett. A 376 (2012) 2015-2022 (arXiv:1008.1575).