Minimal nonergodic directions on genus 2 translation surfaces
arXiv:math/0501286
Abstract
It is well-known that on any Veech surface, the dynamics in any minimal direction is uniquely ergodic. In this paper it is shown that for any genus 2 translation surface which is not a Veech surface there are uncountably many minimal but not uniquely ergodic directions.
15 pages, 2 figures, major simplifications in presentation as recommended by referee, to appear in Ergodic Theory Dynamical Systems