{"paper":{"title":"Unique ergodicity of branched covers of translation surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Elizaveta Shuvaeva, Polina Baron","submitted_at":"2026-06-03T22:31:31Z","abstract_excerpt":"Let $X$ be a finite-area translation surface whose vertical flow is uniquely ergodic. Given a slit joining two nonsingular points of $X$, one can form a branched cyclic cover by gluing $\\mathrm{N}$ copies of $X$ crosswise along the slit. We study when the vertical flow on the resulting cover is uniquely ergodic.\n  We first prove a geometric criterion for unique ergodicity of the branched cover. We show that if, for a sequence of times along the Teichm\\\"uller geodesic, one endpoint of the slit is contained in embedded Euclidean disks of uniformly positive radius that avoid the other endpoint, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05492","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.05492/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}