• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.173-179
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• 2020

Let X be a compact space and Λ a finite index set. We deal with dynamical properties of iterated function systems on X. For an iterated function system 𝓕 on X, we prove that 𝓕 is c-expansive if and only if 𝓕^k is also c-expansive for each k ∈ ℕ. Furthermore we prove that the c-expansiveness of 𝓕 is equivalent to the original expansiveness of the shift map of it.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1421-1431
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• 2021

In this paper we study the preservation of various notions of expansivity in discrete dynamical systems and the induced map for n-fold symmetric products and hyperspaces. Then we give a characterization of a compact metric space admitting hyper N-expansive homeomorphisms via the topological dimension. More precisely, we show that C⁰-generically, any homeomorphism on a compact manifold is not hyper N-expansive for any N ∈ ℕ. Also we give some examples to illustrate our results.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1249-1258
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• 2022

In this study, we show that the strong exponential limit shadowing property (SELmSP, for short), which has been recently introduced, exists on a neighborhood of a hyperbolic set of a diffeomorphism. We also prove that Ω-stable diffeomorphisms and 𝓛-hyperbolic homeomorphisms have this type of shadowing property. By giving examples, it is shown that this type of shadowing is different from the other shadowings, and the chain transitivity and chain mixing are not necessary for it. Furthermore, we extend this type of shadowing property to positively expansive maps with the shadowing property.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.967-979
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• 2019

Chaotic dynamical systems, preferably on a Cantor-like space with some arithmetic operations are considered as good pseudo-random number generators. There are many definitions of chaos, of which Devaney-chaos and pos itive topological entropy seem to be the strongest. Let $A=\{0,1,{\dots},p-1\}$. We define a continuous map on $A^{\mathbb{Z}}$ using addition with a carry, in combination with the shift map. We show that this map gives rise to a dynamical system with positive entropy, which is also Devaney-chaotic: i.e., it is transitive, sensitive and has a dense set of periodic points.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.195-205
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• 2024

In this paper, we consider the set of periodic shadowable points for homeomorphisms of a compact metric space, and we prove that this set satisfies some properties such as invariance and being a G_δ set. Then we investigate implication relations related to sets consisting of shadowable points, periodic shadowable points and uniformly expansive points, respectively. Assume that the set of periodic points and the set of periodic shadowable points of a homeomorphism on a compact metric space are dense in X. Then we show that a homeomorphism has the periodic shadowing property if and only if so is the restricted map to the set of periodic shadowable points. We also give some examples related to our results.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.73-85
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• 1998

This paper deals with the topological stability of continuous maps. First, the notion of local expansion is given and we show that local expansions of compact metric spaces have the shadowing property. Also, we prove that if a continuous surjective map f is a local homeomorphism and local expansion, then f is topologically stable in the class of continuous surjective maps. Finally, we find homeomorphisms which are not topologically stable.

• The Journal of the Korea Contents Association
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• v.13 no.8
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• pp.458-465
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• 2013

The purpose of this research is possible to reduce cost of management and maintenance to realization of smartphone and using data server network technology instead of GPS. Former wireless bus information system was focused on supply side management structure and national spread thus it needs to establish GPS terminal, Windows CE, Window XP embedded and LCD panels which provide only one way communication of information of public traffic information. Therefore, former system management and maintenance cost are very expansive. This research is not use GPS terminal and other hardware equipment but design and realization using smartphone and data network server. This system also provides low cost of management and maintenance. It is not only service downtown area but also out of town and small and medium-sized cities. This system functionally gets a satisfying result user convenience and satisfaction using function of set-up route map, real-time display, and running statically analysis.