Exceptional ergodic directions in Eaton lenses

Mauro Artigiani

doi:10.1007/s11856-017-1509-8

Exceptional ergodic directions in Eaton lenses

Mauro Artigiani

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English (US)
Pages (from-to)	29-56
Number of pages	28
Journal	Israel Journal of Mathematics
Volume	220
Issue number	1
DOIs	https://doi.org/10.1007/s11856-017-1509-8
State	Published - Jun 1 2017
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-017-1509-8

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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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AB - 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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Exceptional ergodic directions in Eaton lenses

Abstract

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