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

Krzysztof Frączek; Martin Schmoll

doi:10.1007/s00220-018-3186-9

paper

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

arXiv:1708.05550 · doi:10.1007/s00220-018-3186-9

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 $Z^{d}$ -covers of quadratic differentials on compact surfaces with vanishing Lyapunov exponents.

44 pages, 30 figures

On ergodicity of foliations on Zd-covers of half-translation surfaces and some applications to periodic systems of Eaton lenses

Abstract

References in corpus (3)

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