{"paper":{"title":"The Hausdorff Dimension of Non-Uniquely Ergodic directions in $\\mathcal{H}(2)$ is almost everywhere $1/2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jayadev S. Athreya, Jon Chaika","submitted_at":"2014-04-17T21:36:39Z","abstract_excerpt":"We show that for almost every (with respect to Masur-Veech measure) $\\omega \\in \\mathcal{H}(2)$, the set of angles $\\theta \\in [0, 2\\pi)$ so that $e^{i\\theta}\\omega$ has non-uniquely ergodic vertical foliation has Hausdorff dimension (and codimension) $1/2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4657","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}