On ergodicity of foliations on $\mathbb Z^d$-covers of half-translation surfaces and some applications to periodic systems of Eaton lenses
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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.
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periodic Eaton lens patterns, ergodicity, quadratic differentials, Lyapunov exponents