Indiscriminate covers of infinite translation surfaces are innocent, not devious
2017 ◽
Vol 39
(8)
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pp. 2071-2127
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Keyword(s):
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, ergodicity and unique ergodicity are preserved under passing to random covers. This work provides a new context for exploring the relationship between recurrence of the Teichmüller flow and ergodic properties of the straight-line flow.
2021 ◽
pp. 253-372
1984 ◽
Vol 56
(3)
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pp. 765-771
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Keyword(s):
2010 ◽
Vol 18
(2)
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pp. 167-174
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2006 ◽
Vol 1
(3)
◽
pp. 270-283
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2015 ◽
Vol 87
(1)
◽
pp. 129-133
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Keyword(s):
Keyword(s):