  We develop a geometrical micro-local analysis of contact Anosov flow, such as
geodesic flow on negatively curved manifold. We use the method of wave-packet
transform discussed in arXiv:1706.09307 and observe that the transfer operator
is well approximated (in the high frequency limit) by the quantization of an
induced transfer operator acting on sections of some vector bundle on the
trapped set. This gives a few important consequences: The discrete eigenvalues
of the generator of transfer operators, called Ruelle spectrum, are structured
into vertical bands. If the right-most band is isolated from the others, most
of the Ruelle spectrum in it concentrate along a line parallel to the imaginary
axis and, further, the density satisfies a Weyl law as the imaginary part tend
to infinity. Some of these results were announced in arXiv:1301.5525.
