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.

Original languageEnglish (US)
Pages (from-to)29-56
Number of pages28
JournalIsrael Journal of Mathematics
Volume220
Issue number1
DOIs
StatePublished - Jun 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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