Equivalent Integrable Metrics on the Sphere with Quartic Invariants

• 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
• 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

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...