  We investigate the influence that classical dynamics has on interference
patterns in coherence experiments. We calculate the time-integrated probability
current through an absorbing screen and the conductance through a doubly
connected ballistic cavity, both in an Aharonov-Bohm geometry with forward
scattering only. We show how interference fringes in the probability current
generically disappear in the case of a chaotic system with small openings, and
how they may persist in the case of an integrable cavity. Simultaneously, the
typical, sample dependent amplitude of the flux-sensitive part $g(\phi)$ of the
conductance survives in all cases, and becomes universal in the case of a
chaotic cavity. In presence of dephasing by fluctuations of the electric
potential in one arm of the Aharonov-Bohm loop, we find an exponential damping
of the flux-dependent part of the conductance, $g(\phi) \propto \exp[-\tau_{\rm
L}/\tau_\phi]$, in term of the traversal time $\tau_{\rm L}$ through the arm
and the dephasing time $\tau_\phi$. This extends previous works on dephasing in
ballistic systems to the case of many conducting channels.
