论文标题
一个动态的thou公式
A dynamical Thouless formula
论文作者
论文摘要
在本文中，我们为$ \ mathrm {gl}（2，\ mathbb {r}）$ cocycles的仿射家庭建立了一个抽象的，动态的th型公式。该结果通过希尔伯特变换，最大的Lyapunov指数和Schrödinger操作员状态的综合密度扩展了经典公式。在这里，状态的综合密度的作用将通过更几何的数量（纤维旋转数）发挥作用。作为此公式的应用，我们提出了对随机线性共生连续性模量的局限性。此外，我们在各种基础动力学上得出了线性共体的光纤旋转数的Hölder-Type连续性。
In this paper we establish an abstract, dynamical Thouless-type formula for affine families of $\mathrm{GL} (2,\mathbb{R})$ cocycles. This result extends the classical formula relating, via the Hilbert transform, the maximal Lyapunov exponent and the integrated density of states of a Schrödinger operator. Here, the role of the integrated density of states will be played by a more geometrical quantity, the fibered rotation number. As an application of this formula we present limitations on the modulus of continuity of random linear cocycles. Moreover, we derive Hölder-type continuity properties of the fibered rotation number for linear cocycles over various base dynamics.
