{"paper":{"title":"Effective Exponential Drifts on Strata of Abelian Differentials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Siyuan Tang","submitted_at":"2025-01-20T15:13:08Z","abstract_excerpt":"We study the dynamics of $SL_{2}(\\mathbb{R})$ on the stratum of translation surfaces $\\mathcal{H}(2)$. In particular, we prove that an orbit of the upper triangular subgroup of $SL_{2}(\\mathbb{R})$ has a discretized dimension of almost $1$ in a direction transverse to the $SL_{2}(\\mathbb{R})$-orbit.\n  The proof proceeds via an effective closing lemma, and the Margulis function technique, which serves as an effective version of the exponential drift on $\\mathcal{H}(2)$. The idea is based on the use of McMullen's classification theorem, together with Lindenstrauss-Mohammadi-Wang's effective equi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.11530","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/2501.11530/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"}