The term "dynamic autoresonance theory" is used to describe the continuing phase locking in driven nonlinear systems with slowly varying parameters. Lazar Friedland (www.fiz.huji.ac.il/~lazar/) has applied this idea to a variety of physical applications. One application is the threshold on migration timescales for capture into resonances in the planar-restricted three-body problem. This theory may explain the small abundance of Kuiper belt objects in the 2:1 resonance with Neptune. I will describe another application involving the opening of gaps in Saturn's rings by resonant satellites