• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.505-512
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• 2005

In this paper, we introduce another statement of a digital $(k_{0}, k_{1})-homeomorphism$ which is suitable for an approach to write an efficient algorithm for discriminating digital images with respect to the digital $(k_{0}, k_{1})-homeomorphism$.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.595-601
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• 1998

In this paper we construct a homeomorphism on a Cantor set which is nearly periodic such that h(a) = b for given a, b $\in$ D$_{p}$. We also give an example which is not almost periodic and we discuss when a homeomorphism on a Cantor set is periodic.c.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.519-536
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• 2000

We construct a stationary, properly ordered Bratteli diagram B=(V,E,$\geq$) so that its Vershik map is isomorphic to Chacon's homeomorphism. It is the simplest stationary, properly ordered Bratteli diagram isomorphic to (Xc, Tc). We also find a primitive and proper substitution of Chacon's transformation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.1
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• pp.1-9
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• 2004

We knew attractive qualities of a rotation number for an analytic diffeomorphism, for example, Arnold tongues and staircase. Numerical computer simulation let us know easily that the pattern of rotation number of a non analytic homeomorphism is similar to its of an analytic homeomorphism for some cases. Also we define new rotation function and investigate it's properties.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.519-529
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• 2004

M. Brown [2] posed an open question on the class of free homeomorphisms as follows: if f is a free homeomorphism of two manifold and k is a positive integer then is $f^{k}$ free\ulcorner In this paper we show that the answer of the open question is true.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.487-495
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• 2005

The main goal of this paper is to prove the digital homotopy lifting theorem with relation to a radius n local homeomorphism.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1171-1184
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• 2010

In this paper, by using fixed point theorems in cones, the existence of positive solutions is considered for nonlinear m-point boundary value problem for the following second-order dynamic equations on time scales $({\phi}(u^{\Delta}))^{\nabla}+a(t)f(t,\;u(t))=0$, t $\in$ (0, T), $u(0)=\sum\limits^{m-2}_{i=1}a_iu(\xi_i)$, $\phi(u^{\Delta}(T))=\sum\limits^{m-2}_{i=1}b_i{\phi}(u^{\Delta}(\xi_i))$, where $\phi$ : R $\rightarrow$ R is an increasing homeomorphism and positive homomorphism and ${\phi}(0)=0$. In [27], we obtained the existence results of the above problem for an increasing homeomorphism and positive homomorphism with sign changing nonlinearity. The purpose of this paper is to supplement with a result in the case when the nonlinear term f is nonnegative, and the most point we must point out for readers is that there is only the p-Laplacian case for increasing homeomorphism and positive homomorphism due to the sign restriction. As an application, one example to demonstrate our results are given.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.477-484
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• 2007

Let h : M ${\rightarrow}$ M be an almost periodic homeomorphism of a compact metric space M onto itself. We prove that h is topologically transitive iff every element of M has a dense orbit. It follows as a corollary that an almost periodic homeomorphism of a compact metric space onto itself can not be chaotic. Some additional related observations on a Cantor set are made.

• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.93-102
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• 1995

In [6], we introduce a hyperbolic homeomorphism on a compact metrizable space and show that a hyperbolic homeomorphism is topologically stable. The purpose of this paper is to study a necessary and sufficient condition for a homeomorphism to be hyperbolic. We get the following theorem.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.255-267
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• 2022

Uniform space is a generalization of metric space. The main purpose of this paper is to extend several results contained in [5, 6] which have for an expansive homeomorphism with the pseudo orbit tracing property(POTP in short) on a compact metric space (X, d) for an expansive homeomorphism with the POTP on a compact uniform space (X, 𝒰). we characterize stable and unstable sets, sink and source and saddle, recurrent points for an expansive homeomorphism which has the POTP on a compact uniform space (X, 𝒰).