Mapping equations are derived, with which nonlinear electron motion in a coherent wave packet for the arbitrary strength of the amplitude is investigated. In a small amplitude wave packet, electrons oscillate in velocity space, reflecting the coherent structure of the wave field. The motion is decorrelated in a moderately large amplitude wave packet, which exhibits a random walk. In a strong amplitude wave packet, electrons are trapped by the wave potential well, when a certain degree of correlation in the motion appears again. In that case, the mapping equations play an active role in the analysis of the particle dynamics because the Fokker-Planck description breaks down there. It is also shown, under a certain condition, that they can be reduced to the standard mapping, which is now well investigated.
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