Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 015, 13 pages      arXiv:2010.03638      https://doi.org/10.3842/SIGMA.2021.015

Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics

Andreas Vollmer ab
a) Institute of Geometry and Topology, University of Stuttgart, 70550 Stuttgart, Germany
b) Dipartimento di Scienze Matematiche (DISMA), Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy

Received October 09, 2020, in final form February 02, 2021; Published online February 17, 2021

Abstract
A non-degenerate second-order maximally conformally superintegrable system in dimension 2 naturally gives rise to a quadric with position dependent coefficients. It is shown how the system's Stäckel class can be obtained from this associated quadric.The Stäckel class of a second-order maximally conformally superintegrable system is its equivalence class under Stäckel transformations, i.e., under coupling-constant metamorphosis.

Key words: Stäckel equivalence; quadrics; superintegrable systems.

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