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arXiv · 1503.02191

Exceptional ergodic directions in Eaton lenses

Mauro Artigiani
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Abstract

We construct examples of ergodic vertical flows in periodic configurations of Eaton lenses of fixed radius. We achieve this by studying a family of infinite translation surfaces that are $\mathbb{Z}^2$-covers of slit tori. We show that the Hausdorff dimension of lattices for which the vertical flow is ergodic is bigger than 3/2. Moreover, the lattices are explicitly constructed.

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Mauro Artigiani. 2015-03-07. Exceptional ergodic directions in Eaton lenses. https://arxiv.org/abs/1503.02191

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