On Robustness of Orbit Spaces for Partially Hyperbolic Endomorphisms  

作　　者：Lin WANG 

机构地区：[1]College of Mathematics and Information Science,Hebei Key Laboratory of Computational Mathematics and Applications,Hebei Normal University

出　　处：《Chinese Annals of Mathematics,Series B》2016年第6期899-914,共16页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11371120);the High-level Personnel for Institutions of Higher Learning in Hebei Province(No.GCC2014052);the Natural Science Foundation of Hebei Province(No.A2013205148)

摘　　要：In this paper, the robustness of the orbit structure is investigated for a partially hyperbolic endomorphism f on a compact manifold M. It is first proved that the dynamical structure of its orbit space （the inverse limit space） M^f of f is topologically quasi-stable under C^0-small perturbations in the following sense： For any covering endomorphism g C^0-close to f, there is a continuous map φ from M^9 to Π-∞^∞ M such that for any {yi}i∈z∈φ（M^9）, yi＋1 and f（yi） differ only by a motion along the center direction. It is then proved that f has quasi-shadowing property in the following sense： For any pseudo-orbit {xi}i∈z, there is a sequence of points {yi}i∈z tracing it, in which yi＋1 is obtained from f（yi） by a motion along the center direction.

关 键 词：Partially hyperbolic endomorphism Orbit space Quasi-stability Quasi-shadowing 

分 类 号：O189[理学—数学]