Resonances of the time evolution (Frobenius-Perron) operator $P$ for phase space densities have recently been shown to play a key role for the interrelations of classical, semiclassical, and quantum dynamics. Efficient methods to determine resonances are thus in demand, in particular, for Hamiltonian systems displaying a mix of chaotic and regular behavior. We present a powerful method based on truncating $P$ to a finite matrix which not only allows us to identify resonances but also the associated phase space structures. It is demonstrated to work well for a prototypical dynamical system.

• Received 11 January 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.3620