  We study two simple real analytic uniformly hyperbolic dynamical systems:
expanding maps on the circle S1 and hyperbolic maps on the torus T2. We show
that the Ruelle-Pollicott resonances which describe time correlation functions
of the chaotic dynamics can be obtained as the eigenvalues of a trace class
operator in Hilbert space L2(S1) or L2(T2) respectively. The trace class
operator is obtained by conjugation of the Ruelle transfer operator in a
similar way quantum resonances are obtained in open quantum systems. We comment
this analogy.
