Almost Periodic Hill's Equation and the Rings of Saturn

Abstract

Incommensurate perturbations of classical orbits lead to an almost periodic Hill's operator whose spectrum, we argue, is a Cantor set, but one with large Lebesgue measure. Applied to the rings of Saturn, this implies that the complex groove structure in the rings approximates a Cantor set. We also emphasize the possible relevance of the sun in producing side gaps which magnify the apparent gap size.