Ergodic Eaton Lens configurations in the plane
Time and place
12:30 PM on Thursday, March 29th, 2018; NAC 6/113
Martin Schmoll (Clemson University)
Abstract
Eaton Lenses are flat lenses that are perfect retroreflectors. We study periodic patterns of non overlapping Eaton lenses in the plane. A light ray moving in the plane furnished with a non overlapping pattern of Eaton lenses will keep a particular direction in the complement of the Eaton lenses. In particular for non overlapping lens patterns it makes sense to consider the ergodicity of the set of light rays parallel to a given direction (in the lens complements). We describe several loops in the "space" of non overlapping Eaton lens patterns parameterized by the light direction (in the lens complements), so that, roughly speaking, for almost every point on each loop, i.e. direction, the family of parallel light rays is ergodic. The mathematical framework we employ to study Eaton lens dynamics are half-translation surfaces. The ergodicity in almost every direction follows from an ergodicity theorem for Zd covers of half-translation surfaces applied to half-translation tori.
This is joint work with Krzysztof Fraczek (Torun).
