Minimality and nonergodicity on a family of flat surfaces in genus 3
arXiv:0801.0466
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.
10 pages, 3 figures