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

arXiv0801.0466MaRDI QIDQ6207995

Publication date: 3 January 2008

Abstract: 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.

Mathematics Subject Classification ID

Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Flows on surfaces (37E35)

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