{"paper":{"title":"Lyapunov exponents for families of rotated linear cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos H. V\\'asquez, Pancho Valenzuela-Henr\\'iquez","submitted_at":"2015-03-24T15:36:35Z","abstract_excerpt":"In this work, we are interested in the study of the upper Lyapunov exponent $\\lambda^+(\\theta)$ associated to the periodic family of cocycles defined by $$A_\\theta(x):=A(x)R_\\theta,\\qquad x\\in X,$$ where $A\\::\\: X\\to \\mathbb{GL}^+(2,\\mathbb{R})$ is a linear cocycle orientation--preser\\-ving and $R_\\theta$ is a rotation of angle $\\theta\\in\\mathbb{R}$. We show that if the cocycle $A$ has dominated splitting, then there exists a non empty open set $\\mathcal{U}$ of parameters $\\theta$ such that the cocycle $A_\\theta$ has dominated splitting and the function $\\mathcal{U}\\ni\\theta\\mapsto\\lambda^+(\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07080","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"}