English

Minimal nonergodic directions on genus 2 translation surfaces

Dynamical Systems 2007-05-23 v3

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.

Cite

@article{arxiv.math/0501286,
  title  = {Minimal nonergodic directions on genus 2 translation surfaces},
  author = {Y. Cheung and H. Masur},
  journal= {arXiv preprint arXiv:math/0501286},
  year   = {2007}
}

Comments

15 pages, 2 figures, major simplifications in presentation as recommended by referee, to appear in Ergodic Theory Dynamical Systems

R2 v1 2026-07-22T17:14:38.794Z