圆展开映射的Cramér距离和离散化Ⅱ：模拟

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Dynamical Systems-An International Journal Pub Date : 2022-06-16 DOI:10.1080/14689367.2023.2236036

Pierre-Antoine Guih'eneuf, M. Monge

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引用次数: 2

摘要

本文介绍了一些与arXiv：2206.07991[math.DS]中对展开图离散化的遍历短期行为的理论研究有关的数值实验顺序为$N$的网格通过该网格上的离散化。在数值模拟的基础上，我们从遍历的角度对数值截断的影响提出了一些猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Cramér distance and discretizations of circle expanding maps II: simulations

This paper presents some numerical experiments in relation with the theoretical study of the ergodic short-term behaviour of discretizations of expanding maps done in arXiv:2206.07991 [math.DS]. Our aim is to identify the phenomena driving the evolution of the Cram\'er 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. Based on numerical simulations we propose some conjectures on the effects of numerical truncation from the ergodic viewpoint.

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来源期刊

Dynamical Systems-An International Journal 物理-力学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal: •Differential equations •Bifurcation theory •Hamiltonian and Lagrangian dynamics •Hyperbolic dynamics •Ergodic theory •Topological and smooth dynamics •Random dynamical systems •Applications in technology, engineering and natural and life sciences