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arXiv · 1706.08649

Sharp Holder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles

Ao Cai·Claire Chavaudret·Jiangong You·Qi Zhou
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Abstract

We show that if the base frequency is Diophantine, then the Lyapunov exponent of a $C^{k}$ quasi-periodic $SL(2,\mathbb{R})$ cocycle is $1/2$-H\"older continuous in the almost reducible regime, if $k$ is large enough. As a consequence, we show that if the frequency is Diophantine, $k$ is large enough, and the potential is $C^k$ small, then the integrated density of states of the corresponding quasi-periodic Schr\"odinger operator is $1/2$-H\"older continuous.

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Ao Cai, Claire Chavaudret, Jiangong You, Qi Zhou. 2017-06-27. Sharp Holder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles. https://arxiv.org/abs/1706.08649

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