  Recent investigations in nonlinear sciences show that not only hyperbolic but
also mixed dynamical systems may exhibit exponential relaxation in the chaotic
regime. The relaxation rates, which lead the decay of probability distributions
and correlation functions, are related to the classical evolution resolvent
(Perron-Frobenius operator) pole logarithm, the so called Pollicott-Ruelle
resonances. In this Brief Report, the leading Pollicott-Ruelle resonances are
calculated analytically for a general class of area-preserving maps. Besides
the leading resonances related to the diffusive modes of momentum dynamics
(slow rate), we also calculate the leading faster rate, related to the angular
correlations. The analytical results are compared to the existing results in
the literature.
