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

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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.
10 pages, 3 figures

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Dynamical Systems, 37D40; 37E35

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http://salesiana.dossiersoluciones.com/handle/123456789/145226

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0801.0466
 http://arxiv.org/abs/0801.0466

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arXiv