Magnetoresistance due to chaos and nonlinear resonances in lateral surface superlattices

We show that chaos and nonlinear resonances are clearly reflected in the magnetotransport in lateral surface superlattices and thereby explain a series of magnetoresistance peaks observed recently in ``antidot'' arrays on semiconductor heterojunctions. We find a mechanism of cyclotron-orbit pinning in an electric field resulting from Kolmogorov-Arnol'd-Moser tori. An experimental verification is suggested in terms of an enhanced cyclotron frequency associated with an anomalously reduced cyclotron radius.