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Hölder continuity of Lyapunov exponent for quasi-periodic Jacobi operators

Kai Tao

2014Bulletin de la Société mathématique de FranceMathematics被引 13

摘要

We consider the quasi-periodic Jacobi operator H x,ω in l 2 (Z)where a(x), b(x) are analytic function on T , b is not identically zero, and ω obeys some strong Diophantine condition.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 existsis Hölder continuous on I with a Hölder exponent β = β(a, b, ω, I).In our derivation we follow the refined version of the Goldstein-Schlag method [GS] developed by Bourgain and Jitomirskaya [BJ].

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DOI：https://doi.org/10.24033/bsmf.2675