• 충청수학회지
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• 제20권3호
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• pp.343-348
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• 2007

In this paper, we show that if a homeomorphism has the pseudo-orbit-tracing-property and its nonwandering set is locally connected, then the limit sets of wandering points whose stable sets have nonempty interior consist of single periodic orbit.

• 충청수학회지
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• 제23권4호
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• pp.871-878
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• 2010

In this paper, we show that if a homeomorphism has the pseudo-orbit-tracing-property and its nonwandering set is locally connected, then the points whose stable sets have nonempty interior are periodic points.

• 충청수학회지
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• 제9권1호
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• pp.107-113
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• 1996

For continuous maps f of the circle to itself, we show that (1) the set of ${\omega}$-limit points is contained in the set of nonwandering points of $f^n$ for all $n{\geq}1$. (2) if the set of turning points of f is finite, then the set of accumulation points of non wandering set is contained in the set of non wandering points of $f^n$ for all $n{\geq}1$.

• 충청수학회지
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• 제35권1호
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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.

• 대한수학회보
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• 제51권2호
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• pp.387-400
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• 2014

We prove that the set of k-type nonwandering points of a Z2-action T can be decomposed into a disjoint union of closed and T-invariant sets $B_1,{\ldots},B_l$ such that $T|B_i$ is topologically k-type transitive for each $i=1,2,{\ldots},l$, if T is expansive and has the shadowing property.

• 충청수학회지
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• 제29권1호
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• pp.171-176
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• 2016

In this article, we study various notions on multi-valued dynamical systems. We first investigate important tools to express the systems, and prove that the notion of chain recurrence is equivalent to the notion of nonwandering set on compact metric spaces.

• 충청수학회지
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• 제5권1호
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• pp.35-47
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• 1992

In this paper we give a necessary condition for a homeomorphism restricted to its nonwandering set to have the shadowing property. Also, we consider a homeomorphism which cannot have the shadowing property.

• Journal of applied mathematics & informatics
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• 제7권3호
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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.

• 충청수학회지
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• 제31권4호
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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.

• 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.