Unique ergodicity of branched covers of translation surfaces
Published in arXiv:2606.05492, 2026
Abstract. Starting with a finite-area translation surface whose vertical flow is uniquely ergodic, we construct branched cyclic covers by gluing copies of the surface crosswise along a slit. We establish a geometric criterion ensuring unique ergodicity of the lifted flow and show that it applies to almost every choice of slit endpoint under a natural geometric condition on the Teichmüller orbit. We also give sufficient conditions in terms of cylinder geometry, introducing the notion of pipe cylinders. Joint with Elizaveta Shuvaeva.
Recommended citation: Polina Baron and Elizaveta Shuvaeva. (2026). "Unique ergodicity of branched covers of translation surfaces." arXiv:2606.05492.
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