• Journal of the Korean Mathematical Society
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• v.33 no.4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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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.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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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 $n{\geq}1$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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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.

• The Pure and Applied Mathematics
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• v.2 no.2
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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)

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1561-1597
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• 2019

In this paper we introduce the notions of topological entropy and topological pressure for non-autonomous iterated function systems (or NAIFSs for short) on countably infinite alphabets. NAIFSs differ from the usual (autonomous) iterated function systems, they are given [32] by a sequence of collections of continuous maps on a compact topological space, where maps are allowed to vary between iterations. Several basic properties of topological pressure and topological entropy of NAIFSs are provided. Especially, we generalize the classical Bowen's result to NAIFSs ensures that the topological entropy is concentrated on the set of nonwandering points. Then, we define the notion of specification property, under which, the NAIFSs have positive topological entropy and all points are entropy points. In particular, each NAIFS with the specification property is topologically chaotic. Additionally, the ${\ast}$-expansive property for NAIFSs is introduced. We will prove that the topological pressure of any continuous potential can be computed as a limit at a definite size scale whenever the NAIFS satisfies the ${\ast}$-expansive property. Finally, we study the NAIFSs induced by expanding maps. We prove that these NAIFSs having the specification and ${\ast}$-expansive properties.

• 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.