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Commun. Korean Math. Soc. 2006; 21(3): 515-526

Printed September 1, 2006

Copyright © The Korean Mathematical Society.

Various inverse shadowing in linear dynamical systems

Taeyoung Choi, Keonhee Lee

Chungnam National University, Chungnam National University

Abstract

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In this paper, we give a characterization of hyperbolic linear dynamical systems via the notions of various inverse shadowing. More precisely it is proved that for a linear dynamical system $f(x)=Ax$ of $\C^n$, $f$ has the $\T_h$-inverse($\T_h$-orbital inverse or $\T_h$-weak inverse) shadowing property if and only if the matrix $A$ is hyperbolic.

Keywords: inverse shadowing, weak inverse shadowing, orbital inverse shadowing, hyperbolicity

MSC numbers: Primary 37C50; Secondary 37D20

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