环面同胚有界平均运动的概念
动力系统
2008-04-29 v2
摘要
二维环面上的保守无理伪旋转半共轭于无理旋转，当且仅当它具有有界平均运动性质 [10]。（此处“无理伪旋转”指具有唯一确定的完全无理旋转向量的环面同胚。）本文旨在进一步探讨这一概念。例如，我们提供了一个反例，表明前述陈述在非保守情形下不成立。此外，我们收集了一系列关于有界平均运动性质失效情形的观察结果。特别是，我们证明了具有无界平均运动的二维环面非游荡无理伪旋转对初始条件具有敏感依赖性。
引用
@article{arxiv.0802.4187,
title = {The concept of bounded mean motion for toral homeomorphisms},
author = {Tobias Jaeger},
journal= {arXiv preprint arXiv:0802.4187},
year = {2008}
}
备注
Some of the results of the previous version were improved in arXiv:0803.2428 . In order to avoid intersections, the remaining material was reorganised, and a new statement concerning sensitive dependence on initial conditions was added. 17 pages, 2 figures