反演极限与Lauwerier吸引子(Ⅰ)

郭峰; 李登辉; 谢建华

doi:10.3879/j.issn.1000-0887.2014.02.009

反演极限与Lauwerier吸引子(Ⅰ)

doi: 10.3879/j.issn.1000-0887.2014.02.009

西南交通大学力学与工程学院, 成都 610031

基金项目: 国家自然科学基金(11172246; 11272268)

详细信息

作者简介:
郭峰 (1976—) 男，山东人，博士生(通讯作者. E-mail: mathguofeng@163.com)

中图分类号: O189; O313
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- 被引次数: 0
出版历程
- 收稿日期: 2013-09-17
- 修回日期: 2013-12-05
- 刊出日期: 2014-02-15

Inverse Limit and Lauwerier Attractor(Ⅰ)

School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P.R.China

Funds: The National Natural Science Foundation of China(11172246;11272268)

摘要

摘要: 通过研究两维的Lauwerier映射,得到Lauwerier奇怪吸引子的一个解析表达式.研究了二次映射的反演极限空间上移位映射的动力学性质,建立了投影映射,运用反演极限空间理论研究Lauwerier映射,证明了Lauwerier映射限制在其吸引子上与二次映射的反演极限上的移位映射是拓扑半共扼的,从而得到Lauwerier吸引子是Devaney意义下混沌的.
- Lauwerier映射 /
- 不稳定流形 /
- 奇怪吸引子 /
- 反演极限 /
- 移位映射
Abstract: A two dimensional Lauwerier mapping was studied and an analytical expression of the strange attractor was obtained. The dynamic properties of the shift map on the inverse limit space of the quadratic mapping were investigated. The projection mapping was established. Then the Lauwerier mapping was studied based on the theory of inverse limit space. It is proved that the Lauwerier mapping restricted to its attractor is topologically semi-conjugate to the shift map on the inverse limit space of the quadratic mapping; therefore the Lauwerier strange attractor is chaotic in the sense of Devaney.
- lauwerier mapping /
- unstable manifold /
- strange attractor /
- inverse limit space /
- shift map

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参考文献(16)

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