Equivalent Integrable Metrics on the Sphere with Quartic Invariants

DOI10.3842/SIGMA.2022.094arXiv2201.09576MaRDI QIDQ6388997

Publication date: 24 January 2022

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.

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Constrained dynamics, Dirac's theory of constraints (70H45) Canonical transformations in symplectic and contact geometry (53D22) Symplectic and canonical mappings (37J11) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

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