• Title, Summary, Keyword: shadowing

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CONTINUOUS SHADOWING AND INVERSE SHADOWING FOR FLOWS

  • Lee, Keonhee;Lee, Manseob;Lee, Zoonhee
    • 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.

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TOPOLOGICAL STABILITY OF INVERSE SHADOWING SYSTEMS

  • Lee, Keonhee;Lee, Joonhee
    • 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.

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DENSITY OF D-SHADOWING DYNAMICAL SYSTEM

  • Kim, J.M.;Kim, S.G.
    • 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.

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Measures on Improving Korean Language Skills by Using Shadowing Techniques (섀도잉(shadowing)기법을 활용한 한국어 수업 방안)

  • Hyun, Nam Ji
    • Journal of Korean language education
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    • v.29 no.2
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    • pp.49-72
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    • 2018
  • The purpose of this study is to introduce an efficient measure in Korean language education for learners of Korean by applying shadowing techniques which focus on improving not only listening and speaking skills but also reading and writing skills. First of all, the study discusses about the definition of shadowing along with the effect of shadowing. The second part will be about examining the proposed method related to shadowing technique which is comprised of original shadowing techniques and other techniques transformed from the original. Thirdly, the paper will be discussing background information of the shadowing technique in previous researches and experiments using shadowing techniques in Korean language education. Finally, there will be an introduction of learning measures that apply to skill unification. Most of the previous researches of the shadowing technique were limited to a few students with only mid-to-high level learners while this method could cover up to a wide range of learners. The most effective way of learning a foreign language would firstly be the suggested method and the focus should be on repetition and practice of the learners.

ON THE DENSITY OF VARIOUS SHADOWING PROPERTIES

  • Koo, Namjip;Tsegmid, Nyamdavaa
    • Communications of the Korean Mathematical Society
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    • v.34 no.3
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    • pp.981-989
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    • 2019
  • In this paper we deal with some shadowing properties of discrete dynamical systems on a compact metric space via the density of subdynamical systems. Let $f:X{\rightarrow}X$ be a continuous map of a compact metric space X and A be an f-invariant dense subspace of X. We show that if $f{\mid}_A:A{\rightarrow}A$ has the periodic shadowing property, then f has the periodic shadowing property. Also, we show that f has the finite average shadowing property if and only if $f{\mid}_A$ has the finite average shadowing property.

WEAK INVERSE SHADOWING AND GENERICITY

  • Choi, Tae-Young;Kim, Sung-Sook;Lee, Keon-Hee
    • 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.

INVERSE SHADOWING FOR EXPANSIVE FLOWS

  • Lee, Keon-Hee;Lee, Zoon-Hee
    • 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.

SOME SHADOWING PROPERTIES OF THE SHIFTS ON THE INVERSE LIMIT SPACES

  • Tsegmid, Nyamdavaa
    • 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.

INVERSE SHADOWING PROPERTY OF MORSE-SMALE SYSTEMS

  • Choi, Taeyoung;Lee, Keonhee
    • 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.

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