• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.53-63
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• 2000

The inverse shadowing property of a dynamical system is an "inverse" form of the shadowing property of the system. Recently, Kloeden and Ombach proved that if an expansive system on a compact manifold has the shadowing property then it has the inverse shadowing property. In this paper, we study topological stability of the inverse shadowing dynamical systems. In particular, we show that if an expansive system on a compact manifold has the inverse shadowing property then it is topologically stable, and so it has the shadowing property.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.1
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• pp.61-73
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• 2002

We consider the inverse shadowing property of a dynamical system which is an "inverse" form of the shadowing property of the system. In particular, we show that every Morse-Smale system f on a compact smooth manifold has the inverse shadowing property with respect to the class $\mathcal{T}_h(f)$ of continuous methods generated by homeomorphisms, but the system f does not have the inverse\mathrm{T} shadowing property with respect to the class $\mathcal{T}_c(f)$ of continuous methods.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.43-52
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• 2006

We study the genericity of the first weak inverse shadowing property and the second weak inverse shadowing property in the space of homeomorphisms on a compact metric space, and show that every shift homeomorphism does not have the first weak inverse shadowing property but it has the second weak inverse shadowing property.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.297-310
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• 2007

The notions of continuous shadowing and inverse shadowing for flows are introduced, and show that an expansive flow on a compact manifold with the shadowing property has the continuous shadowing property. Moreover it is proved that the continuous shadowing property implies the inverse shadowing property.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.91-101
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• 2005

In this paper, we give the notion of the D-shadowing property, D-inverse shadowing property for dynamical systems. and investigate the density of D-shadowing dynamical systems and the D-inverse shadowing dynamical systems. Moreover we study some relationships between the D-shadowing property and other dynamical properties such as expansivity and topological stability.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.703-713
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• 2003

We extend the notion of inverse shadowing defined for diffeomorphisms to flows, and show that an expansive flow on a compact manifold with the shadowing property has the inverse shadowing property with respect to the classes of continuous methods. As a corollary we obtain that a hyperbolic flow also has the inverse shadowing property with respect to the classes of continuous methods.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.577-585
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• 2007

We introduce the inverse shadowing property of geometric Lorenz flows and prove that the geometric Lorenz flows do not have the inverse shadowing property.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.461-466
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• 2018

$Let\;f:X{\rightarrow}X$ be a continuous surjection of a compact metric space X and let ${\sigma}_f:X_f{\rightarrow}X_f$ be the shift map on the inverse limit space $X_f$ constructed by f. We show that if a continuous surjective map f has some shadowing properties: the asymptotic average shadowing property, the average shadowing property, the two side limit shadowing property, then ${\sigma}_f$ also has the same properties.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.411-418
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• 2009

In this paper we introduce the notions of strict persistence and weakly strict persistence which are stronger than those of persistence and weak persistence, respectively, and study their relations with shadowing property. In particular, we show that the weakly strict persistence and the weak inverse shadowing property are locally generic in Z(M).

• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.515-526
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• 2006

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 ${\mathbb{C}^n}$, f has the ${\tau}_h$ inverse(${\tau}_h-orbital$ inverse or ${\tau}_h-weak$ inverse) shadowing property if and only if the matrix A is hyperbolic.