Equivalent Integrable Metrics on the Sphere with Quartic Invariants
Exactly Solvable and Integrable Systems
2022-12-07 v4 Mathematical Physics
Dynamical Systems
math.MP
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.
Cite
@article{arxiv.2201.09576,
title = {Equivalent Integrable Metrics on the Sphere with Quartic Invariants},
author = {Andrey V. Tsiganov},
journal= {arXiv preprint arXiv:2201.09576},
year = {2022}
}