Minimal nonergodic directions on genus 2 translation surfaces
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- January 2005
- DOI:
- 10.48550/arXiv.math/0501286
- arXiv:
- arXiv:math/0501286
- Bibcode:
- 2005math......1286C
- Keywords:
-
- Mathematics - Dynamical Systems;
- 37D40;
- 37E35
- E-Print:
- 15 pages, 2 figures, major simplifications in presentation as recommended by referee, to appear in Ergodic Theory Dynamical Systems