{"paper":{"title":"On the Size of the Resonant Set for the Products of 2x2 Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Benjamin Seeger, Deborah Unger, Jeffrey Allen","submitted_at":"2011-06-15T08:24:47Z","abstract_excerpt":"For {\\theta} \\in [0, 2{\\pi}), consider the rotation matrix R? and h = ({\\lambda}, 0; 0, 0), {\\lambda} > 1. Let W_n({\\theta}) denote the product of m R?'s and n h's with the condition m \\leq [\\epsilon\\astn], (0 < \\epsilon < 1). We analyze the measure of the set of {\\theta} for which ||W_n({\\theta})|| \\geq {\\lambda}?^(n*{\\delta}), (0 < {\\delta} < 1). This can be regarded as a model problem for the so-called Bochi-Fayad conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2903","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"}