Quantum zeta function for perturbed cat maps

The behavior of semiclassical approximations to the spectra of perturbed quantum cat maps is examined as the perturbation parameter brings the corresponding classical system into the nonhyperbolic regime. The approximations are initially accurate but large errors are found to appear in the traces and in the coefficients of the characteristic polynomial after nonhyperbolic structures appear. Nevertheless, the eigenvalues obtained from them remain accurate up to large perturbations. (c) 1995 American Institute of Physics.