拟跟踪性与有限型移位  

Quasi-shadowing and Shifts of Finite Type

作　　者：王林 王昕晟 WANG LIN;WANG XINSHENG(College of Applied Mathematics,Shanri University of Finance and Economics,Taiyuan 030006,China;Department of Mathematics,Shantou University,Shantou 515063,China)

机构地区：[1]山西财经大学应用数学学院,太原030006 [2]汕头大学数学系,汕头515063

出　　处：《应用数学学报》2024年第4期549-566,共18页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:11771118,11801336);山西省基础研究计划项目(批准号:202303021211140);汕头大学科学研究启动基金(批准号:NTF22020)资助课题。

摘　　要：本文主要引入系统关于叶集(叶层)拟跟踪性的拓扑定义,并在黎曼流形上得到该定义与通常意义下系统关于叶层拟跟踪性的定义是等价的.同时,我们分别在紧致完全不连通Hausdorff空间上和黎曼流形上讨论了系统关于叶集(叶层)的拟跟踪性和有限型移位序列的逆极限之间的联系.此外,我们还给出了因子映射保持拟跟踪性的一个充分条件.In this paper,we mainly introduce a topological definition of quasi-shadowing property with respect to a leaf-set(or a foliation)on a dynamical system,which is equivalent to the general definition of quasi-shadowing property with respect to a foliation on Riemannian manifolds.At the same time,we discuss the relationship between the quasi-shadowing property with respect to a leaf-set(or a foliation)and an inverse limit of a sequence of shifts of finite type on the compact Hausdorff totally disconnected spaces and Riemannian manifolds respectively.In addition,we give a sufficient condition for the factor maps to preserve quasi-shadowing property.

关 键 词：不变叶层 拟跟踪 有限型移位 

分 类 号：O193[理学—数学]