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arXiv:0801.0466 [math.DS]AbstractReferencesReviewsResources

Minimality and nonergodicity on a family of flat surfaces in genus 3

Emanuel Nipper

Published 2008-01-03Version 1

We prove that a certain family of flat surfaces in genus 3 does not fulfill Veech's Dichotomy. These flat surfaces provide uncountably many minimal but nonergodic directions. The conditions on this family are a combinatorical one and an irrationality condition. The Arnoux-Yoccoz surface fulfills this conditions.

Comments: 10 pages, 3 figures
Categories: math.DS
Subjects: 37D40, 37E35
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