论文标题
Lyapunov指数的单位光盘和扰动理论上的随机Möbius动力学
Random Möbius dynamics on the unit disc and perturbation theory for Lyapunov exponents
论文作者
论文摘要
随机绘制的$ 2 \ times 2 $矩阵通过Möbius变换在Riemann Sphere上诱导随机动力学。考虑到这种动力学仅限于单位光盘的情况，并且由随机旋转受到进一步随机术语的随机旋转给出，具体取决于两个竞争的小参数，因此确定了随机动力学系统的不变（furstenberg）度量。结果与Lyapunov指数的扰动理论相关，这与一维离散随机schrödinger运算符相关。
Randomly drawn $2\times 2$ matrices induce a random dynamics on the Riemann sphere via the Möbius transformation. Considering a situation where this dynamics is restricted to the unit disc and given by a random rotation perturbed by further random terms depending on two competing small parameters, the invariant (Furstenberg) measure of the random dynamical system is determined. The results have applications to the perturbation theory of Lyapunov exponents which are of relevance for one-dimensional discrete random Schrödinger operators.
