• 제목/요약/키워드: nonwandering map

검색결과 6건 처리시간 0.017초

NONWANDERING POINTS OF A MAP ON THE CIRCLE

  • Bae, Jong-Sook;Cho, Seong-Hoon;Min, Kyung-Jin;Yang, Seung-Kab
    • 대한수학회지
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    • 제33권4호
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    • pp.1115-1122
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    • 1996
  • In study of the dynamics of a map f from a topological space X to itself, a central role is played by the various recursive properties of the points of X. One such property is periodicity. A weaker property is that of being nonwandering. Intermediate recursive properties include almost periodicity and recurrence.

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ON THE ERGODIC SHADOWING PROPERTY THROUGH UNIFORM LIMITS

  • Namjip Koo;Hyunhee Lee
    • 충청수학회지
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    • 제37권2호
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    • pp.75-80
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    • 2024
  • In this paper, we study some dynamics of the uniform limits of sequences in dynamical systems on a noncompact metric space. We show that if a sequence of homeomorphisms on a noncompact metric space has the uniform ergodic shadowing property, then the uniform limit also has the ergodic shadowing property. Then we apply this result to nonwandering maps.

A NOTE ON RECURSIVE SETS FOR MAPS OF THE CIRCLE

  • Cho, Seong Hoon
    • 충청수학회지
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    • 제13권1호
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    • pp.101-107
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    • 2000
  • For a continuous map f of the circle to itself, we show that if P(f) is closed, then ${\Gamma}(f)$ is closed, and ${\Omega}(f)={\Omega}(f^n)$ for all n > 0.

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$\omega$-LIMIT SETS FOR MAPS OF THE CIRCLE

  • Cho, Seong-Hoon
    • 대한수학회논문집
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    • 제15권3호
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    • pp.549-553
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    • 2000
  • For a continuous map of the circle to itself, we give necessary and sufficient conditions for the $\omega$-limit set of each nonwandering point to be minimal.

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RECURSIVE PROPERTIES OF A MAP ON THE CIRCLE

  • Cho, Seong-Hoon;Min, Kyung-Jin;Yang, Seung-Kab
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제2권2호
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    • pp.157-162
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    • 1995
  • Let I be the interval, $S^1$ the circle and let X be a compact metric space. And let $C^{circ}(X,\;X)$ denote the set of continuous maps from X into itself. For any f$f\in\;C\circ(X,\;X),\;let\;P(f),\;R(f),\;\Gamma(f),\;\Lambda(f)\;and\;\Omega(f)$ denote the collection of the periodic points, recurrent points, ${\gamma}-limit{\;}points,{\;}{\omega}-limit$ points and nonwandering points, respectively.(omitted)

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