  Resolved images suggest that asymmetric structures are a common feature of
cold debris disks. While planets close to these disks are rarely detected,
their hidden presence and gravitational perturbations provide plausible
explanations for some of these features. To put constraints on the properties
of yet undetected planetary companions, we aim to predict what features such a
planet imprints in debris disks undergoing continuous collisional evolution. We
discuss the basic equations, analytic approximations and timescales governing
collisions, radiation pressure and secular perturbations. In addition, we
combine our numerical model of the collisional evolution of the size and
spatial distributions in debris disks with the gravitational perturbation by a
single planet. We find that the distributions of orbital elements in the disks
are strongly dependent on grain sizes. Secular precession is differential with
respect to involved semi-major axes and grain sizes. This leads to observable
differences between the big grains tracing the parent belt and the small grains
in the trailing halo. Observations at different wavelengths can be used to
constrain the properties of a possible planet.
