• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.423-431
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• 2016

Images and inverse images of (almost) stable cubic sets are discussed. We show that the image and inverse image of stable cubic sets are also stable. Conditions for the image of almost cubic sets to be an almost cubic set are provided. The complement, the P-union and the P-intersection of (inverse) images of (almost) stable cubic sets are considered.

• 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.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.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1091-1097
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• 2009

In this paper, we investigate the extensions of generalized stable rings. It is shown that a ring R is a generalized stable ring if and only if R has a complete orthogonal set {e$_1$, . . . , e$_n$} of idempotents such that e$_1$Re$_1$, . . . , e$_n$Re$_n$ are generalized stable rings. Also, we prove that a ring R is a generalized stable ring if and only if R[[X]] is a generalized stable ring if and only if T(R,M) is a generalized stable ring.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.23-28
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• 2016

In this paper, we obtain close characterizations of flows near a saddle set which is one of the interesting unstable closed sets. Also, we consider some conditions that closed sets are to be stable.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.453-459
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• 2019

In this paper, we analyze the behaviour of flows near closed sets with compact boundary which contains no semi-orbits. Also, we give a condition that a closed invariant set is to be asymptotically stable.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.2
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• pp.137-145
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• 2004

We give characterization of ${\Omega}$-stable diffeomorphisms via the notions of weak inverse shadowing. More precisely, it is proved that the $C^1$ interior of the set of diffeomorphisms with the weak inverse shadowing property with respect to the class $\mathcal{T}_h$ coincides with the set of ${\Omega}$-stable diffeomorphisms.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.871-881
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• 2008

In this paper, we study the core stability of the dominating set game which has arisen from the cost allocation problem related to domination problem on graphs. Let G be a graph whose neighborhood matrix is balanced. Applying duality theory of linear programming and graph theory, we prove that the dominating set game corresponding to G has the stable core if and only if every vertex belongs to a maximum 2-packing in G. We also show that for dominating set games corresponding to G, the core is stable if it is large, the game is extendable, or the game is exact. In fact, the core being large, the game being extendable and the game being exact are shown to be equivalent.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1505-1521
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• 2008

In this paper, we give a characterization of the structurally stable vector fields via the notion of orbital inverse shadowing. More precisely, it is proved that the $C^1$ interior of the set of $C^1$ vector fields with the orbital inverse shadowing property coincides with the set of structurally stable vector fields. This fact improves the main result obtained by K. Moriyasu et al. in [15].

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.509-524
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• 2019

Let Act(G, X) be the set of all continuous actions of a finitely generated group G on a compact metric space X. In this paper, we study the concepts of topologically stable points and continuous shadowable points of a group action T ∈ Act(G, X). We show that if T is expansive then the set of continuous shadowable points is contained in the set of topologically stable points.