Comment on `conservative discretizations of the Kepler motion'

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We show that the exact integrator for the classical Kepler motion, recently found by Kozlov (J. Phys. A: Math. Theor.} 40 (2007) 4529-4539), can be derived in a simple natural way (using well known exact discretization of the harmonic oscillator). We also turn attention on important earlier references, where the exact discretization of the 4-dimensional isotropic harmonic oscillator has been applied to the perturbed Kepler problem.