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Consider a monokinetic probability measure on phase space.In this lecture,we study the structure of the monokinetic measure and the associated position density when transported by a regular Hamiltonian flow.In particular,we give estimates on the number of folds on which the obtaned measure is concentrated.We explain how our results can be applied to investigate the classical limit of the Schrodinger equation by using the formalism of Wigner measures.Our formalism includes initial momentum profiles with much lower regularity than required by the WKB method.Finally,we discuss a few examples showinq that our results are sharp.