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 \({\mathbb{Z}^d}\)-covers of quadratic differentials on compact surfaces with vanishing Lyapunov exponents.
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Communicated by J. Marklof
K. Frączek: The first author was partially supported by the Narodowe Centrum Nauki Grant 2014/13/B/ST1/03153.
M. Schmoll: The second author was partially supported by Simons Collaboration Grant 318898.
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Frączek, K., Schmoll, M. On Ergodicity of Foliations on \({\mathbb{Z}^d}\)-Covers of Half-Translation Surfaces and Some Applications to Periodic Systems of Eaton Lenses. Commun. Math. Phys. 362, 609–657 (2018). https://doi.org/10.1007/s00220-018-3186-9
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DOI: https://doi.org/10.1007/s00220-018-3186-9