论文标题
关于随机分段仿射间隔同态的固定措施的维度
On the dimension of stationary measures for random piecewise affine interval homeomorphisms
论文作者
论文摘要
我们研究了迭代功能系统（被认为是随机动力学系统）的固定措施，这些措施由两个分段仿射间隔同构形态组成，称为Alsedà--Misiurewicz（AM）系统。我们证明，对于一组开放的参数，AM系统的唯一非原子固定度量严格小于$ 1 $。特别是，我们获得了这些措施的奇异性，从2014年起部分回答了Alsedà和Misiurewicz的问题。
We study stationary measures for iterated function systems (considered as random dynamical systems) consisting of two piecewise affine interval homeomorphisms, called Alsedà--Misiurewicz (AM) systems. We prove that for an open set of parameters, the unique non-atomic stationary measure for an AM-system has Hausdorff dimension strictly smaller than $1$. In particular, we obtain singularity of these measures, answering partially a question of Alsedà and Misiurewicz from 2014.
