Abstract
Consider a monokinetic probability measure on the phase space , i.e. where U (in) is a vector field on R (N) and rho (in) a probability density on R (N) . Let I broken vertical bar (t) be a Hamiltonian flow on R (N) x R (N) . In this paper, we study the structure of the transported measure and of its integral in the xi variable denoted rho(t). In particular, we give estimates on the number of folds in , on which mu (() t) 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 U (in) with much lower regularity than required by the WKB method. Finally, we discuss a few examples showing that our results are sharp.