Generalized Stäckel Transform and Reciprocal Transformations for Finite-Dimensional Integrable Systems
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We present a multiparameter generalization of the Stäckel transform (the latter is also known as the coupling-constant metamorphosis) and show that under certain conditions this generalized Stäckel transform preserves the Liouville integrability, noncommutative 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 Stäckel transform.
21 pages, LaTeX 2e, no figures; major revision; Propositions 2 and 7 and several new references added
21 pages, LaTeX 2e, no figures; major revision; Propositions 2 and 7 and several new references added