论文标题
真实线上的随机动态系统
Random dynamical systems on a real line
论文作者
论文摘要
我们研究了实际线路上的随机动态系统，考虑到每个动力系统以及逆图生成的系统。我们表明，此类系统的正向行为和反向行为之间存在双重性，将它们分为四个类（就动态和固定度量方面而言）。这类似于[0,1]上平滑动力学的结果，该结果是根据终点的Lyapunov指数确定的。但是，我们的论点纯粹是拓扑的，因此我们的结果适用于真实线同构的一般情况。
We study random dynamical systems on the real line, considering each dynamical system together with the one generated by the inverse maps. We show that there is a duality between forward and inverse behaviour for such systems, splitting them into four classes (in terms of both dynamical and stationary measure aspects). This is analogous to the results already known for the smooth dynamics on [0,1], established in terms of the Lyapunov exponents at the endpoints; however, our arguments are purely topological, and thus our result is applicable to the general case of homeomorphisms of the real line.
