论文标题
cramér的距离和圆扩展地图的离散化I：理论
Cramér distance and discretizations of circle expanding maps I: theory
论文作者
论文摘要
本文旨在研究圆形扩展地图的离散化的千古短期行为。更确切地说，我们证明了$ t $ f $ $ f $的$ t $ t $ t $ t $ t $ t $ f $ t $ t $ th $ t $ th y时，当$ n $的网格上，当$ n $上的订单$ n $ the $ n $ t $ t $时，$ t $ t $固定时，$ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $。这是在动力学上的一些显式通用假设下完成的，并且度量之间的距离通过\ emph {cramér}距离的平均值来衡量。该证明是基于对相应线性化问题的研究，在该问题中，该问题被转化为$ t $中尺寸指数的Tori上的等效术语。 与这项工作相关的数值研究在Arxiv：2206.08000 [Math.ds]中提出。
This paper is aimed to study the ergodic short-term behaviour of discretizations of circle expanding maps. More precisely, we prove some asymptotics of the distance between the $t$-th iterate of Lebesgue measure by the dynamics $f$ and the $t$-th iterate of the uniform measure on the grid of order $N$ by the discretization on this grid, when $t$ is fixed and the order $N$ goes to infinity. This is done under some explicit genericity hypotheses on the dynamics, and the distance between measures is measured by the mean of \emph{Cramér} distance. The proof is based on a study of the corresponding linearized problem, where the problem is translated into terms of equirepartition on tori of dimension exponential in $t$. A numerical study associated to this work is presented in arXiv:2206.08000 [math.DS].
