{"paper":{"title":"Random product of quasi-periodic cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jamerson Bezerra, Mauricio Poletti","submitted_at":"2019-07-01T14:19:58Z","abstract_excerpt":"Given a finite set of quasi-periodic cocycles the random product of them is defined as the random composition according to some probability measure.\n  We prove that the set of $C^r$, $0\\leq r \\leq \\infty$ (or analytic) $k+1$-tuples of quasi periodic cocycles taking values in $SL_2(\\mathbb{R})$ such that the random product of them has positive Lyapunov exponent contains a $C^0$ open and $C^r$ dense subset which is formed by $C^0$ continuity point of the Lyapunov exponent\n  For $k+1$-tuples of quasi periodic cocycles taking values in $GL_d(\\mathbb{R})$ for $d>2$, we prove that if one of them is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00815","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"}