MICZ-Kepler systems in noncommutative space and duality of force laws

In this paper, we analyze the modification of integrable models in the k-deformed space-time. We show that two-dimensional isotropic oscillator problem, Kepler problem and MICZ-Kepler problem in k-deformed space-time admit integrals of motion as in the commutative space. We also show that the duality equivalence between k-deformed Kepler problem and k-deformed two-dimensional isotropic oscillator explicitly, by deriving Bohlin-Sundman transformation which maps these two systems. These results are valid to all orders in the deformation parameter.