• East Asian mathematical journal
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• 제27권5호
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• pp.521-525
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• 2011

We use a weaker version of the celebrated Newton-Kantorovich theorem [3] reported by us in [1] to find solutions of discrete dynamical systems involving operators with chaotic behavior. Our results are obtained by extending the application of the shadowing lemma [4], and are given under the same computational cost as before [4]-[6].

• 충청수학회지
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• 제17권2호
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• pp.137-145
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• 2004

We give characterization of ${\Omega}$-stable diffeomorphisms via the notions of weak inverse shadowing. More precisely, it is proved that the $C^1$ interior of the set of diffeomorphisms with the weak inverse shadowing property with respect to the class $\mathcal{T}_h$ coincides with the set of ${\Omega}$-stable diffeomorphisms.

• 대한수학회지
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• 제58권2호
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• pp.439-449
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• 2021

In this paper, we introduce the notions of expansiveness, shadowing property and topological stability for group actions on metric spaces and give a version of Walters's stability theorem for group actions on locally compact metric spaces. Moreover, we show that if G is a finitely generated virtually nilpotent group and there exists g ∈ G such that if Tg is expansive and has the shadowing property, then T is topologically stable.

• 충청수학회지
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• 제35권4호
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• pp.329-333
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• 2022

In this paper we investigate some properties concerning the set of shadowable points for homeomorphisms. Then we show that the almost shadowing property is preserved by a topological conjugacy between homeomorphisms. Also, we give an example to illustrate our results.

• 대한수학회보
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• 제60권4호
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• pp.1131-1139
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• 2023

In this paper, we introduce the concept of ω-expansive of random map on compact metric spaces 𝓟. Also we introduce the definitions of positively, negatively shadowing property and shadowing property for two-sided RDS. Then we show that if 𝜑 is ω-expansive and has the shadowing property for ω, then 𝜑 is topologically stable for ω.

• 충청수학회지
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• 제25권4호
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• pp.725-730
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• 2012

Let $f$ be a diffeomorphism of a closed $C^{\infty}$ manifold M. We show that $C^1$-generically, if $f$ has the shadowing property on a robustly transitive set, then it is hyperbolic.

• 충청수학회지
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• 제29권1호
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• pp.151-155
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• 2016

In this paper, we show that if a continuum-wise expansive homeomorphism on a compact connected metric space is shadowing then it is topologically stable. This generalizes the main result of [4].

• 충청수학회지
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• 제26권1호
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• pp.45-52
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• 2013

We show that a nontrivial transitive set is $C^1$-stably limit shadowable if and only if the transitive set is hyperbolic.

• 대한수학회논문집
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• 제24권1호
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• pp.127-144
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• 2009

Let f be a diffeomorphism of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper we introduce the notion of $C^1$-stable inverse shadowing for a closed f-invariant set, and prove that (i) the chain recurrent set $\cal{R}(f)$ of f has $C^1$-stable inverse shadowing property if and only if f satisfies both Axiom A and no-cycle condition, (ii) $C^1$-generically, the chain component $C_f(p)$ of f associated to p is hyperbolic if and only if $C_f(p)$ has the $C^1$-stable inverse shadowing property.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2009년도 IWAIT
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• pp.429-434
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• 2009

We introduce an instant and intuitive shadowing technique for CACAni System. In traditional 2D Anime, since all frames are drawn by hand it takes long time to create an entire animation sequence. CACAni System reduces such a production cost by automatic inbetweening and coloring. In this paper, we develop a shadowing technique that enables CACAni users to easily create shadow for character or object in the image. The only inputs required are sequences of character or object layers drawn in CACAni System with alpha value. Shadows are automatically rendered on a virtual plane based on these inputs. They can then be edited by CACAni users. Achieving this, CACAni System is able to handle instant shadowing and intuitive editing in a short time.