• Title/Summary/Keyword: Nonwandering set and chain recurrent set

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THE SPECTRAL DECOMPOSITION FOR FLOWS ON TVS-CONE METRIC SPACES

  • Lee, Kyung Bok
    • Journal of the Chungcheong Mathematical Society
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    • v.35 no.1
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    • pp.91-101
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    • 2022
  • We study some properties of nonwandering set Ω(𝜙) and chain recurrent set CR(𝜙) for an expansive flow which has the POTP on a compact TVS-cone metric spaces. Moreover we shall prove a spectral decomposition theorem for an expansive flow which has the POTP on TVS-cone metric spaces.

ON THE LIMIT SETS AND THE BASIC SETS OF CHAIN RECURRENT SETS

  • Koo, Ki-Shik
    • Journal of applied mathematics & informatics
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    • v.7 no.3
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    • pp.1029-1038
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    • 2000
  • In this paper, we show that if x is a positively Lyapunov stable point of an expansive homeomorphism with the pseudo-orbit-tracing-property, then x is a periodic point or its positive limit set consists of only one periodic orbit, and their periods are predictable. We give a necessary and sufficient condition that a basic set is to be a sink or source. Also, we consider some dynamical properties of basic sets.

SHADOWABLE POINTS FOR FINITELY GENERATED GROUP ACTIONS

  • Kim, Sang Jin;Lee, Keonhee
    • Journal of the Chungcheong Mathematical Society
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    • v.31 no.4
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    • pp.411-420
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    • 2018
  • In this paper we introduce the notion of shadowable points for finitely generated group actions on compact metric spaace and prove that the set of shadowable points is invariant and Borel set and if chain recurrent set contained shadowable point set then it coincide with nonwandering set. Moreover an action $T{\in}Act(G, X)$ has the shadowing property if and only if every point is shadowable.