On ergodicity of foliations on $\mathbb Z^d$-covers of half-translation surfaces and some applications to periodic systems of Eaton lenses

Loading...
Thumbnail Image

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

We consider the geodesic flow defined by periodic Eaton lens patterns in the plane and discover ergodic ones among those. The ergodicity result on Eaton lenses is derived from a result for quadratic differentials on the plane that are pull backs of quadratic differentials on tori. Ergodicity itself is concluded for $\mathbbZ^d$-covers of quadratic differentials on compact surfaces with vanishing Lyapunov exponents.

Description

Keywords

periodic Eaton lens patterns, ergodicity, quadratic differentials, Lyapunov exponents

Citation

Collections

Endorsement

Review

Supplemented By

Referenced By