符号系统的2类跟踪及其应用  

Two Types of Shadowing for Symbolic Systems and Their Applications

作　　者：朱玉峻[1] 张金莲[1] 郑宏文[1] 

机构地区：[1]河北师范大学数学与信息科学学院,河北石家庄050016

出　　处：《河北师范大学学报（自然科学版）》2004年第2期109-112,共4页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金资助项目(10371030)

摘　　要：证明了符号动力系统具有Lipschitz跟踪性和极限跟踪性.作为其应用,借助拓扑共轭证明了Smale马蹄,二次映射在其双曲不变集上具有(相对C1小扰动一致的)极限跟踪性;借助Lipschitz共轭证明了线性的马蹄在其双曲不变集上具有Lipschitz跟踪性.To show that the symbolic systems have both the Lipschitz shadowing property and the limit shadowing property.As applications,prove that both the Smale's horseshoes and the quadratic maps have the limit shadowing property on their hyperbolic invariant sets,and this property is also 'uniform'with respect to C ~1-perturbation,also prove that the 'linear'　horseshoes have the Lipschitz shadowing property on their hyperbolic sets.

关 键 词：符号动力系统 Lipschitz跟踪 极限跟踪 SmaIe马蹄 

分 类 号：O193[理学—数学] O415[理学—基础数学]