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Exceptional ergodic directions in Eaton lenses

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Abstract

We construct examples of ergodic vortical flows in periodic configurations of Eaton lenses of fixed radius. We achieve this by studying a family of infinite translation surfaces that are ℤ2-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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Authors and Affiliations

  1. Centro di Ricerca Matematica, Ennio De Giorgi Collegio Puteano, Scuola Normale Superiore, Piazza dei Cavalieri, 3 I-56100, Pisa, Italy

    Mauro Artigiani

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  1. Mauro Artigiani
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Correspondence to Mauro Artigiani.

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Research supported by a University of Bristol graduate scholarship

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Artigiani, M. Exceptional ergodic directions in Eaton lenses. Isr. J. Math. 220, 29–56 (2017). https://doi.org/10.1007/s11856-017-1509-8

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  • DOI: https://doi.org/10.1007/s11856-017-1509-8

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