  We study the spectrum of transfer operators associated to various dynamical
systems. Our aim is to obtain precise information on the discrete spectrum. To
this end we propose a unitary approach. We consider various settings where new
information can be obtained following different branches along the proposed
path. These settings include affine expanding Markov maps, uniformly expanding
Markov maps, non-uniformly expanding or simply monotone maps, hyperbolic
diffeomorphisms. We believe this approach could be greatly generalized.
