  We consider a simple model of partially expanding map on the torus. We study
the spectrum of the Ruelle transfer operator and show that in the limit of high
frequencies in the neutral direction (this is a semiclassical limit), the
spectrum develops a spectral gap, for a generic map. This result has already
been obtained by M. Tsujii (05). The novelty here is that we use semiclassical
analysis which provides a different and quite natural description. We show that
the transfer operator is a semiclassical operator with a well defined
"classical dynamics" on the cotangent space. This classical dynamics has a
"trapped set" which is responsible for the Ruelle resonances spectrum. In
particular we show that the spectral gap is closely related to a specific
dynamical property of this trapped set.
