Noncommutative Kepler Dynamics: symmetry groups and bi-Hamiltonian structures

Abstract

Integrals of motion are constructed from noncommutative (NC) Kepler dynamics, generating SO(3), SO(4), and SO(1, 3) dynamical symmetry groups. The Hamiltonian vector field is derived in action-angle coordinates, and the existence of a hierarchy of bi-Hamiltonian structures is highlighted. Then, a family of Nijenhuis recursion operators is computed and discussed.