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

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dc.contributor.authorVollmer, Andreas
dc.date.accessioned2025-12-25T13:21:43Z
dc.date.issued2021
dc.description.abstractA 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.
dc.description.sponsorshipThe author is indebted to Jonathan Kress, Joshua Capel, and Konrad Schobel for many discussions on superintegrability, Stackel transforms, and numerous related topics, and thanks the anonymous referees for contributing valuable suggestions that led to improvements of this paper. A special thank you goes to Konrad Schobel for helpful comments on the manuscript. This paper was principally written when the author was a fellow of the German Research Foundation Deutsche Forschungsgemeinschaft (DFG): Andreas Vollmer acknowledges funding from a DFG research fellowship with the project number 353063958, as well as through a subsequent return fellowship. Andreas Vollmer thanks the University of Stuttgart and the University of New South Wales for their hospitality.
dc.identifier.citationStäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics. Andreas Vollmer. SIGMA 17 (2021), 015, 13 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2021.015
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 14H70; 70H06; 30F45
dc.identifier.otherarXiv:2010.03638
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/211173
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleStäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2021, том 17, випуск за цей рік