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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1503.07080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-24T15:36:35Z","cross_cats_sorted":[],"title_canon_sha256":"da2f59954400d7a07870e37f911ff57310e946b9dac5b5c351ca276bb39e68c6","abstract_canon_sha256":"17b0400b395ace5c749e49b59c361c42bb55ff6940c8fbd7221c87fef06f2c65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:29.428638Z","signature_b64":"5nofEWYSTT+ognjP80EdrOQqXfgjEZEUKtI/UPOwmrE8kqaub48qCPqwoE9xC0/dGxrVlb/MsRofdp460s9SBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a4777c47ddc67bafa6efc65b132b9ee2adbc38c008ae3dfc41d9d14031817bc","last_reissued_at":"2026-05-18T02:20:29.428286Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:29.428286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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