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Symmetry, Integrability and Geometry: Methods and Applications, 2022, Volume 18, 094, 19 pp.
DOI: https://doi.org/10.3842/SIGMA.2022.094 (Mi sigma1890) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Equivalent Integrable Metrics on the Sphere with Quartic Invariants

Andrey V. Tsiganov

St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (378 kB) Citations (1)
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DOI: https://doi.org/10.3842/SIGMA.2022.094
Abstract: We discuss canonical transformations relating well-known geodesic flows on the cotangent bundle of the sphere with a set of geodesic flows with quartic invariants. By adding various potentials to the corresponding geodesic Hamiltonians, we can construct new integrable systems on the sphere with quartic invariants.
Keywords: integrable metrics, canonical transformations, two-dimensional sphere.
Funding agency Grant number
Russian Science Foundation 21-11-00141
The work was supported by the Russian Science Foundation (project 21-11-00141).
Received: March 31, 2022; in final form December 4, 2022; Published online December 6, 2022
Bibliographic databases:
Document Type: Article
MSC: 37J35, 70H06, 70H45
Language: English
Citation: Andrey V. Tsiganov, “Equivalent Integrable Metrics on the Sphere with Quartic Invariants”, SIGMA, 18 (2022), 094, 19 pp.
Citation in format AMSBIB
\Bibitem{Tsi22}
\by Andrey~V.~Tsiganov
\paper Equivalent Integrable Metrics on the Sphere with Quartic Invariants
\jour SIGMA
\yr 2022
\vol 18
\papernumber 094
\totalpages 19
\mathnet{http://mi.mathnet.ru/sigma1890}
\crossref{https://doi.org/10.3842/SIGMA.2022.094}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4517949}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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