Almost Periodic Szegő Cocycles with Uniformly Positive Lyapunov Exponents
David Damanik, Helge Krueger
我们展示的例子，几乎周期Verblunsky系数赫尔曼的次谐波参数适用，并产生相关的李雅普诺夫指数一致有界远离零。
We exhibit examples of almost periodic Verblunsky coefficients for which Herman's subharmonicity argument applies and yields that the associated Lyapunov exponents are uniformly bounded away from zero.
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Uniform Szego Cocycles Over Strictly Ergodic Subshifts
我们认为遍历家庭的Verblunsky系数产生的最小非周期子移位。Simon证明了单位圆上的相关概率测度具有零勒贝格测度的本质支撑.我们证明了这一点的一大类subshift，即那些满足Boshernitzan的条件。这是通过相关的基本支持相应的Szego上循环的一致收敛性属性。
Positive Lyapunov Exponents for Quasiperiodic Szego cocycles
本文首先利用Herman-Avila-Bochi公式得到了遍历Szego余圈的平均李雅普诺夫指数公式。然后利用加速度方法构造了一类解析的具有一致正李雅普诺夫指数的拟周期Szego余圈.最后，利用文[Y]中的主要定理，给出了一类C1拟周期双边Verblunsky系数的测度的支集的勒贝格测度的估计.用同样的方法，我们也恢复了具有非常数实解析势的Schrodinger上循环的[S-S]结果，并得到了任意固定Brjuno频率和一定C1势的非一致双曲性结果.
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