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Resonances of the (Frobenius-Perron) evolution operator P for phase-spacedensities have recently attracted considerable attention, in the context ofinterrelations between classical and quantum dynamics. We determine theseresonances as well as eigenvalues of P for Hamiltonian systems with a mixedphase space, by truncating P to finite size in a Hilbert space of phase-spacefunctions and then diagonalizing. The corresponding eigenfunctions arelocalized on unstable manifolds of hyperbolic periodic orbits for resonancesand on islands of regular motion for eigenvalues. Using information drawn fromthe eigenfunctions we reproduce the resonances found by diagonalization througha variant of the cycle expansion of periodic-orbit theory and as rates ofcorrelation decay.Comment: 18 pages, 7 figure

Resonances of the Frobenius-Perron operator for a Hamiltonian map with a mixed phase space