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Reciprocal transformations for Stackel-related Liouville integrable systems

Maciej Blaszak·Artur Sergyeyev
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Abstract

We consider the Stäckel transform, also known as the coupling-constant metamorphosis, which under certain conditions turns a Hamiltonian dynamical system into another such system and preserves the Liouville integrability. We show that the corresponding transformation for the equations of motion is nothing but the reciprocal transformation of a special form and we investigate the properties of this transformation. This result is further applied for the study of the $k$-hole deformations of the Benenti systems or more general seed systems.

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Maciej Blaszak, Artur Sergyeyev. 2006-07-25. Reciprocal transformations for Stackel-related Liouville integrable systems. https://arxiv.org/abs/nlin/0607057

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