Reciprocal transformations for Stackel-related Liouville integrable systems

Details Reciprocal transformations for Stackel-related Liouville integrable systems Reciprocal transformations for Stackel-related Liouville integrable systems

2006-07-25

arxiv.org/abs/nlin/0607057v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, no figures

Scientific paper

We consider the St\"ackel 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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