Rapid fluctuation for topological dynamical systems

被引：1
|
作者：
Huang, Yu [1 ]
Zhou, Yi [2 ]
机构：
[1] Zhongshan Sun Yat sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China
[2] Zhongshan Sun Yat sen Univ, Dept Biomed Engn, Zhongshan Sch Med, Guangzhou 510080, Guangdong, Peoples R China
来源：
FRONTIERS OF MATHEMATICS IN CHINA | 2009年 / 4卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Rapid fluctuation; quasi-shift invariant set; topological horseshoe; Hausdorff dimension; LINEAR WAVE-EQUATION; VAN; SNAPSHOTS; CHAOS; MAPS;
D O I：
10.1007/s11464-009-0030-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we introduce a new notion called rapid fluctuation to characterize the complexity of a general topological dynamical system. As a continuation of the former work [Huang, Chen, Ma, J. Math. Anal. Appl., 2006, 323: 228-252], here we prove that a Lipschitz dynamical system defined on a compact metric space has a rapid fluctuation if it has either a quasi shift invariant set or a topological horseshoe. As an application, the rapid fluctuation of a discrete predator-prey model is considered.
引用
收藏
页码：483 / 494
页数：12
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