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

Twisted debris: how differential secular perturbations shape debris disks