  Resonances of the (Frobenius-Perron) evolution operator P for phase-space
densities have recently attracted considerable attention, in the context of
interrelations between classical and quantum dynamics. We determine these
resonances as well as eigenvalues of P for Hamiltonian systems with a mixed
phase space, by truncating P to finite size in a Hilbert space of phase-space
functions and then diagonalizing. The corresponding eigenfunctions are
localized on unstable manifolds of hyperbolic periodic orbits for resonances
and on islands of regular motion for eigenvalues. Using information drawn from
the eigenfunctions we reproduce the resonances found by diagonalization through
a variant of the cycle expansion of periodic-orbit theory and as rates of
correlation decay.
