Equivalent Integrable Metrics on the Sphere with Quartic Invariants

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.

References in corpus (2)

• New bi-Hamiltonian systems on the plane
• Bäcklund transformations for the nonholonomic Veselova system