Reciprocal transformations for Stackel-related Liouville integrable systems

2006/07/25 by Maciej Blaszak, Blaszak, Maciej, Artur Sergyeyev +1
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #math-ph #math.MP #math.SG #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0607057

12 pages, no figures

arxiv created 2006/07/25 · arxiv updated 2009/12/01

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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