Exceptional ergodic directions in Eaton lenses

Mauro Artigiani

doi:10.1007/s11856-017-1509-8

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 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 language	English
Pages (from-to)	29-56
Number of pages	28
Journal	Israel Journal of Mathematics
Volume	220
Issue number	1
Early online date	5 May 2017
DOIs	https://doi.org/10.1007/s11856-017-1509-8
Publication status	Published - Jun 2017

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title = "Exceptional ergodic directions in Eaton lenses",

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 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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N2 - 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 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.

AB - 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 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.

U2 - 10.1007/s11856-017-1509-8

DO - 10.1007/s11856-017-1509-8

M3 - Article (Academic Journal)

SN - 0021-2172

VL - 220

SP - 29

EP - 56

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -

Exceptional ergodic directions in Eaton lenses

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