{"paper":{"title":"Orbits in Teichm\\\"uller dynamics admits a critical exponent gap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Omri Nisan Solan","submitted_at":"2024-11-14T02:56:45Z","abstract_excerpt":"McMullen '03 constructs a collection of orbits $\\mathrm{SL}_2(\\mathbb{R}).x$ in $\\mathcal{H}(1,1)$ with infinitely generated stabilizers $\\mathrm{stab}_{\\mathrm{SL}_2(\\mathbb{R})}(x)$. We prove a gap in the set of critical exponents of stabilizers of $\\mathrm{SL}_2(\\mathbb{R})$-orbits in $\\mathcal{H}_g$: for every $x\\in \\mathcal{H}_g$, either $\\mathrm{stab}_{\\mathrm{SL}_2(\\mathbb{R})}(x)$ is a lattice, or we have a uniform bound on the critical exponent $\\delta(\\mathrm{stab}_{\\mathrm{SL}_2(\\mathbb{R})}(x)) \\le 1-\\varepsilon_g$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09144","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/2411.09144/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"}