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Minimal non-ergodic directions on genus-2 translation surfaces

  • YITWAH CHEUNG (a1) and HOWARD MASUR (a2)
  • DOI: http://dx.doi.org/10.1017/S0143385705000465
  • Published online: 17 March 2006
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. The theorem can be applied to certain billiard tables.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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