TY - JOUR
AU1 - Wang, Lin
AU2 - Zhang, Jinlian
AB - In this paper, the shadowing property of 1-dimensional subsystems for suspension of ℤk\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$\mathbb {Z}^{k}$\end{document}-actions is investigated. The concepts of pseudo orbit and shadowing property of 1-dimensional subsystems for suspension of ℤk\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$\mathbb {Z}^{k}$\end{document}-actions are introduced. It is shown that the shadowing properties of these subsystems and their induced nonautonomous dynamical systems are equivalent. For the suspension ΦT of a smooth ℤk\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$\mathbb {Z}^{k}$\end{document}-action T, we show that ΦT has the shadowing property along any Anosov subspace. As an application, we show that ΦT is structurally stable along any Anosov subspace.
TI - Shadowing Property of 1-dimensional Subsystems for Suspension of ℤk\documentclass[12pt]{minimal}				\usepackage{amsmath}				\usepackage{wasysym}				\usepackage{amsfonts}				\usepackage{amssymb}				\usepackage{amsbsy}				\usepackage{mathrsfs}				\usepackage{upgreek}				\setlength{\oddsidemargin}{-69pt}				\begin{document}$\mathbb {Z}^{k}$\end{document}-actions
JF - Journal of Dynamical and Control Systems
DO - 10.1007/s10883-022-09625-x
DA - 2023-10-01
UR - https://www.deepdyve.com/lp/springer-journals/shadowing-property-of-1-dimensional-subsystems-for-suspension-of-k-2i0XcplIGz
SP - 1203
EP - 1217
VL - 29
IS - 4
DP - DeepDyve
ER -