The dynamics of a charged particle in a two-dimensional space under the influence of a nonuniform, periodic magnetic field, similar to the magnetic induction inside an extremely type-II superconductor in the vortex state, is studied. The Hamiltonian for this model is found to be classically nonintegrable. A study of classical trajectories shows a global transition from a confined chaotic motion on tori for small amplitude of the periodic modulation, to an extended chaotic system that fills phase space uniformly, for strong modulations. The classical dynamics is confronted with a semiclassical Gaussian wave-packet approach and a time-dependent quantum-mechanical (QM) propagation scheme, for the same Hamiltonian. When the magnetic field modulation is small the envelopes of both the semiclassical and the exact QM autocorrelation functions are found to be Gaussian at short times. For a strong magnetic field modulation the envelope of the semiclassical autocorrelation function crosses over to a decaying exponential, determined by the characteristic Lyapunov exponent of the chaotic motion. It deviates significantly from the exact QM autocorrelation function, which retains the Gaussian envelope. The relatively strong recursion peaks of the latter may indicate a quantum localization effect. \textcopyright{} 1996 The American Physical Society.