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

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

2008-01-03

arxiv.org/abs/0801.0466v1

Mathematics

Dynamical Systems

10 pages, 3 figures

Scientific paper

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.

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