Indiscriminate covers of infinite translation surfaces are innocent, not devious

  title={Indiscriminate covers of infinite translation surfaces are innocent, not devious},
  author={W. Hooper and R. Trevi{\~n}o},
  journal={arXiv: Dynamical Systems},
  • W. Hooper, R. Treviño
  • Published 2015
  • Mathematics
  • arXiv: Dynamical Systems
  • We consider the interaction between passing to finite covers and ergodic properties of the straight-line flow on finite area translation surfaces with infinite topological type. Infinite type provides for a rich family of degree $d$ covers for any integer $d>1$. We give examples which demonstrate that passing to a finite cover can destroy ergodicity, but we also provide evidence that this phenomenon is rare. We define a natural notion of a random degree $d$ cover and show that, in many cases… CONTINUE READING
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