{"paper":{"title":"Projective cocycles over SL(2,R) actions: measures invariant under the upper triangular group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alex Eskin, Amie Wilkinson, Christian Bonatti","submitted_at":"2017-09-08T03:33:37Z","abstract_excerpt":"We consider the action of $SL(2,\\mathbb{R})$ on a vector bundle $\\mathbf{H}$ preserving an ergodic probability measure $\\nu$ on the base $X$. Under an irreducibility assumption on this action, we prove that if $\\hat\\nu$ is any lift of $\\nu$ to a probability measure on the projectivized bunde $\\mathbb{P}(\\mathbf{H})$ that is invariant under the upper triangular subgroup, then $\\hat \\nu$ is supported in the projectivization $\\mathbb{P}(\\mathbf{E}_1)$ of the top Lyapunov subspace of the positive diagonal semigroup. We derive two applications. First, the Lyapunov exponents for the Kontsevich-Zoric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02521","kind":"arxiv","version":3},"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"}