ON THE CHARACTERIZATION OF HOMOCLINIC CLASSES BY MEANS OF THE SHADOWING PROPERTY

自Anosov和Bowen的著作以来，伪轨道遮蔽性的概念经常出现在动力系统理论的几个分支中，并在研究中起着重要作用。动力系统阴影理论的最新发展是非常引人注目的；事实上，阴影理论不仅是动力系统数值研究的基础，而且在动力系统定性理论中也产生了许多重要的结果。本研究旨在从动力系统的微分几何理论出发，对具有阴影性质的动力系统或子系统进行表征。

Since Anosov and Bowen's works, the notion of the pseudo-orbit shadowing property very often appears in the several branches of the theory of dynamical systems, and usually plays an important role in the investigation. The latest developments of the shadowingtheory of dynamical systems are very remarkable; in fact, the shadowing theory is not only a base of numerical study of dynamical systems but also gives rise to lots of important consequences in qualitative theory of dynamical systems. The purpose of this research project is to characterize the dynamical systems or subsystems possessing the shadowing property from view point of the differential geometric theory of dynamical systems.