  We analyze the dynamics of a charged particle moving in the presence of
spatially-modulated magnetic fields. From Poincare surfaces of section and
Liapunov exponents for characteristic trajectories we find that the fraction of
pinned and runaway quasiperiodic orbits {\em vs}. chaotic orbits depends
strongly on the ratio of cyclotron radius to the structure parameters, as well
as on the amplitude of the modulated field. We present a complete
characterization of the dynamical behavior of such structures, and investigate
the contribution to the magnetoconductivity from all different orbits using a
classical Kubo formula. Although the DC conductivity of the system depends
strongly on the pinned and runaway trajectories, the frequency response
reflects the topology of all different orbits, and even their unusual temporal
behavior.
