A canonical Kepler map for the dynamics of a particle in a 1/r potential in the presence of an external time-dependent field is discussed. For linearly polarized fields in one dimension and for circularly polarized fields in two dimensions a consistent derivation of the map is given to first order in the field strength F. The results are compared with the map obtained by direct numerical integration of the equations of motion.
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Michael Nauenberg (1990) studied this question.
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