• 충청수학회지
• /
• 제29권4호
• /
• pp.651-655
• /
• 2016

In this paper, we show that if a quasi-Anosov diffeomorphism has the various types of shadowing property then it is Anosov.

• 충청수학회지
• /
• 제29권4호
• /
• pp.657-661
• /
• 2016

Let $f:X{\rightarrow}X$ be a continuous surjection of a compact metric space and let ($X_f,{\tilde{f}}$) be the inverse limit of a continuous surjection f on X. We show that for a continuous surjective map f, if f has the asymptotic average, the average shadowing, the ergodic shadowing property then ${\tilde{f}}$ is topologically transitive.

• 대한수학회보
• /
• 제40권4호
• /
• pp.703-713
• /
• 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.

• 충청수학회지
• /
• 제15권1호
• /
• pp.61-73
• /
• 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.

• 충청수학회지
• /
• 제30권4호
• /
• pp.381-385
• /
• 2017

Let (X, d) be a compact metric space with metric d and let f : $X{\rightarrow}X$ be a continuous map. In this paper, we consider that for a subset ${\Lambda}$, a map f has the eventual shadowing property if and only if f has the eventual shadowing property on ${\Lambda}$. Moreover, a map f has the eventual shadowing property if and only if f has the eventual shadowing property in ${\Lambda}$.

• 충청수학회지
• /
• 제31권4호
• /
• pp.461-466
• /
• 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.

• Nonlinear Functional Analysis and Applications
• /
• 제28권4호
• /
• pp.929-942
• /
• 2023

In this paper, we discuss topological ergodic shadowing property and topological pseudo-orbital specification property of iterated function systems(IFS) on uniform spaces. We show that an IFS on a sequentially compact uniform space with topological ergodic shadowing property has topological shadowing property. We define the notion of topological pseudo-orbital specification property and investigate its relation to topological ergodic shadowing property. We find that a topologically mixing IFS on a compact and sequentially compact uniform space with topological shadowing property has topological pseudo-orbital specification property and thus has topological ergodic shadowing property.

• 충청수학회지
• /
• 제25권4호
• /
• pp.739-745
• /
• 2012

We show that if a symplectic diffeomorphism has the $C^1$-robustly orbital shadowing property, then the diffeomorphism is Anosov.

• 대한수학회보
• /
• 제53권2호
• /
• pp.581-588
• /
• 2016

Komuro [3] proved that geometric Lorentz attractor does not satisfy the shadowing property. In this paper we study the condition under which geometric Lorenz attractor has the orbital shadowing property that is weaker than the shadowing property.

• 충청수학회지
• /
• 제32권2호
• /
• pp.165-170
• /
• 2019

$C^1$ generically, if a diffeomorphism $f:M{\rightarrow}M$ of a closed smooth Riemannian manifold M has the asymptotic average shadowing property or the average shadowing property then f has a decomposition property.