Steinlein-Walther双曲集上的反伪轨跟踪性

Inverse shadowing property on Steinlein-Walther hyperbolic set

用反伪轨跟踪性的概念来刻画了Banach空间上的C1映射在一种弱化的双曲集即Steinlein-Walther双曲集上的一种稳定性,得到了广义的跟踪性引理.设H为一个Banach空间,φ:V→H为H的一个开子集V上的C1映射,如果T V为φ的Steinlein-Walther双曲集合,则φ在T上关于连续方法的类θs具有反伪轨跟踪性.

In this paper,a kind of stability of C^1 map on a weak kind of hyperbolic set is given,that is,Steinlein-Walther hyperbolic set,via the notion of inverse shadowing,obtain a generalized shadowing lemma.Let H be a Banach space,φ：V→H a C^1 map on a open subset V of H.Assume that T belong to V is a Steinlein-Walther hyperbolic set of φ.Then φ has the inverse shadowing property with respect to a continuous method θs on T.