论文标题
通过不可接受的lyapunov规范的可接受性来描述调整指数二分法
Description of tempered exponential dichotomies by admissibility with no Lyapunov norms
论文作者
论文摘要
调速指数二分法为随机动力学系统制定了不均匀的双曲线。它是通过lyapunov规范定义的一对函数类别的可接受性来描述的，用于满足乘法性ergodic定理的假设（缩写为MET）的假设），可以通过不使用Lyapunov Norm的一对的可接受性来描述。但是，尚不清楚如何在给出调整的指数二分法之前选择合适的Lyapunov规范，并且有一些随机系统的例子不是MET-SYSTEM，但具有调整的指数二分法。在本文中，我们对一般随机系统的钢化指数二分法进行了描述，这可能不是满足系统，纯粹是通过没有Lyapunov Norms的三对函数类别的可衡量可接受性。此外，限制了MET-Systems，我们获得了只有一个没有Lyapunov规范的一对的简单描述。最后，我们使用结果来证明参数随机系统的钢化指数二分法的粗糙度，并给出了相关投影对参数的连续依赖性。
Tempered exponential dichotomy formulates the nonuniform hyperbolicity for random dynamical systems. It was described by admissibility of a pair of function classes defined with Lyapunov norms, For MET-systems (systems satisfying the assumptions of multiplicative ergodic theorem (abbreviated as MET)), it can be described by admissibility of a pair without a Lyapunov norm. However, it is not known how to choose a suitable Lyapunov norms before a tempered exponential dichotomy is given, and there are examples of random systems which are not MET-systems but have a tempered exponential dichotomy. In this paper we give a description of tempered exponential dichotomy for general random systems, which may not be MET-systems, purely by measurable admissibility of three pairs of function classes with no Lyapunov norms. Further, restricting to the MET-systems, we obtain a simpler description of only one pair with no Lyapunov norms. Finally, we use our results to prove the roughness of tempered exponential dichotomies for parametric random systems and give a Hölder continuous dependence of the associated projections on the parameter.
