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Prequantum dynamics was introduced in the 70s by Kostant, Souriau and Kirillov as an intermediate between classical and quantum dynamics. In common with the classical dynamics, prequantum dynamics transports functions on phase space, but adds some phases which are important in quantum interference effects. In the case of hyperbolic dynamical systems, it is believed that the study of the prequantum dynamics will give a better understanding of the quantum interference effects for large time, anddoi:10.3934/jmd.2007.1.255 fatcat:t52b3pw23red3jo7itiovj4krq