{"paper":{"title":"Introduction to Teichm\\\"uller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Matheus, Giovanni Forni","submitted_at":"2013-11-12T12:43:31Z","abstract_excerpt":"This text is an expanded version of the lecture notes of a minicourse (with the same title of this text) delivered by the authors in the Bedlewo school \"Modern Dynamics and its Interaction with Analysis, Geometry and Number Theory\" (from 4 to 16 July, 2011).\n  In the first part of this text, i.e., from Sections 1 to 5, we discuss the Teichm\\\"uller and moduli space of translation surfaces, the Teichm\\\"uller flow and the SL(2,R)-action on these moduli spaces and the Kontsevich-Zorich cocycle over the Teichm\\\"uller geodesic flow. We sketch two applications of the ergodic properties of the Teichm\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2758","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":""},"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"}