Multiparameter Generalization of the Stackel Transform, Deformations of Separation Curves and Reciprocal Transformations

Abstract:
We present a multiparameter generalization of the Stackel transform, also known as the coupling-constant metamorphosis. We show that under certain conditions this transformation preserves the Liouville integrability and superintegrability. The corresponding transformation for the equations of motion proves to be nothing but a reciprocal transformation of a special form, and we investigate the properties of this reciprocal transformation.

Finally, we show that the Hamiltonians of the systems possessing separation curves of apparently very different form can be related through a suitably chosen generalized Stackel transform.

This is joint work with Maciej Blaszak. For more details see arXiv:0706.1473.