{"paper":{"title":"H\\\"older continuity of Lyapunov exponent for quasi-periodic Jacobi operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kai Tao","submitted_at":"2011-08-18T13:06:16Z","abstract_excerpt":"We consider the quasi-periodic Jacobi operator $H_{x,\\omega}$ in $l^2(\\mathbb{Z})$ $(H_{x,\\omega}\\phi)(n) = -b(x+(n+1)\\omega)\\phi(n+1) - b(x+n\\omega)\\phi(n-1) + a(x+n\\omega)\\phi(n) = E\\phi(n),\\ n\\in\\mathbb{Z},$ where $a(x),\\ b(x)$ are analytic function on $\\mathbb{T}$, $b$ is not identically zero, and $\\omega$ obeys some strong Diophantine condition.\n  We consider the corresponding unimodular cocycle. We prove that if the Lyapunov exponent $L(E)$ of the cocycle is positive for some $E=E_0$, then there exists $\\rho_0=\\rho_0(a,b,\\omega,E_0)$, $\\beta=\\beta(a,b,\\omega)$ such that $|L(E)-L(E')|<|E-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3747","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"}