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.

References in corpus (4)

• Late time acceleration in a deformed phase space model of dilaton cosmology
• Non-commutative multi-dimensional cosmology
• Late time acceleration in a non-commutative model of modified cosmology
• On Geometry and Symmetry of Kepler Systems. I