具有双曲不变集系统的极限跟踪性  

LIMIT SHADOWING PROPERTY OF DIFFEOMORPHISMS WITH HYPERBOLIC INVARIANT SETS

作　　者：朱玉峻[1] 王玲书[1] 张金莲[1] 

机构地区：[1]河北师范大学数学与信息科学学院,石家庄050016

出　　处：《数学年刊（A辑）》2004年第5期613-620,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10371030);河北师范大学博士基金(No.L2003B05)资助的项目.

摘　　要：本文证明了Riemann流形上的微分同胚f在其双曲不变集附近具有相对于C1小扰动一致的极限 跟踪性.还证明了如果f是C1-结构稳定的,则,具有极限跟踪性.This paper considers the limit shadowing property for diffeomorphisms on a Riemannian manifold. Let f be a diffeomorphism. It is shown that (1) f has the limit shadowing property with respect to some δ>0 on a neighborhood of the hyperbolic set, and this property is 'uniform' with respect to C1-perturbation; (2) if f is C1-structurally stable, then f has the limit shadowing property with respect to some δ> 0.

关 键 词：渐近伪轨 极限跟踪性 双曲集 结构稳定性 

分 类 号：O193[理学—数学]