Sharp $frac12$-H"older continuity of the Lyapunov exponent at the bottom of the spectrum for a class of Schr"odinger cocycles
Sharp $frac12$-H"older continuity of the Lyapunov exponent at the bottom of the spectrum for a class of Schr"odinger cocycles
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一类 Schr"odinger 余循环的谱底部的李亚普诺夫指数的夏普 $frac12$-H"旧连续性
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发表时间：
2018
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通讯作者：
Thomas Ohlson Timoudas
中科院分区：
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作者：
Jordi;Thomas Ohlson Timoudas
我们考虑了一个类似的双曲性均匀消失的场景，如Bjerkl“ov和Saprykina（2008，Nonlinearity 21），其中证明了不变稳定和不稳定丛之间的最小距离对参数具有线性幂律依赖性。在这种情况下，我们证明了李雅普诺夫指数是尖锐的$frac12$-H“老连续的。特别是，我们表明，在大耦合区域中，具有唯一非退化最小值的势的Schr 'odinger上循环的李雅普诺夫指数在谱的最低能量以下是尖锐的$frac12$-H' older连续的。
We consider a similar type of scenario for the disappearance of uniform of hyperbolicity as in Bjerkl"ov and Saprykina (2008, Nonlinearity 21), where it was proved that the minimum distance between invariant stable and unstable bundles has a linear power law dependence on parameters. In this scenario we prove that the Lyapunov exponent is sharp $frac12$-H"older continuous. In particular, we show that the Lyapunov exponent of Schr"odinger cocycles with a potential having a unique non-degenerate minimum, is sharp $frac12$-H"older continuous below the lowest energy of the spectrum, in the large coupling regime.