Equivalent Integrable Metrics on the Sphere with Quartic Invariants

We discuss canonical transformations relating well-known geodesic flows on the cotangent bundle of the sphere to 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 quarti...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2022
Main Author: Tsiganov, Andrey V.
Format: Article
Language:English
Published: Інститут математики НАН України 2022
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/211810
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Equivalent Integrable Metrics on the Sphere with Quartic Invariants. Andrey V. Tsiganov. SIGMA 18 (2022), 094, 19 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Tsiganov, Andrey V.
author_facet Tsiganov, Andrey V.
citation_txt Equivalent Integrable Metrics on the Sphere with Quartic Invariants. Andrey V. Tsiganov. SIGMA 18 (2022), 094, 19 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We discuss canonical transformations relating well-known geodesic flows on the cotangent bundle of the sphere to 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.
first_indexed 2026-03-13T11:13:36Z
format Article
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-13T11:13:36Z
publishDate 2022
publisher Інститут математики НАН України
record_format dspace
spelling Tsiganov, Andrey V.
2026-01-12T10:14:54Z
2022
Equivalent Integrable Metrics on the Sphere with Quartic Invariants. Andrey V. Tsiganov. SIGMA 18 (2022), 094, 19 pages
1815-0659
2020 Mathematics Subject Classification: 37J35; 70H06; 70H45
arXiv:2201.09576
https://nasplib.isofts.kiev.ua/handle/123456789/211810
https://doi.org/10.3842/SIGMA.2022.094
We discuss canonical transformations relating well-known geodesic flows on the cotangent bundle of the sphere to 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.
We are very grateful to the referees for their thorough analysis of the manuscript, constructive suggestions, and proposed corrections, which certainly led to a more profound discussion of the results. The work was supported by the Russian Science Foundation (project 21-11-00141).
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Equivalent Integrable Metrics on the Sphere with Quartic Invariants
Article
published earlier
spellingShingle Equivalent Integrable Metrics on the Sphere with Quartic Invariants
Tsiganov, Andrey V.
title Equivalent Integrable Metrics on the Sphere with Quartic Invariants
title_full Equivalent Integrable Metrics on the Sphere with Quartic Invariants
title_fullStr Equivalent Integrable Metrics on the Sphere with Quartic Invariants
title_full_unstemmed Equivalent Integrable Metrics on the Sphere with Quartic Invariants
title_short Equivalent Integrable Metrics on the Sphere with Quartic Invariants
title_sort equivalent integrable metrics on the sphere with quartic invariants
url https://nasplib.isofts.kiev.ua/handle/123456789/211810
work_keys_str_mv AT tsiganovandreyv equivalentintegrablemetricsonthespherewithquarticinvariants