• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.529-535
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• 2019

In this article, we study the dynamics of invertible iterated function systems on compact spaces. We prove the equivalences for the notions of expansiveness on invertible iterated function systems.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.927-933
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• 2020

We characterize Möbius functions mapping the unit disc of the complex plane contractively into itself. We then give a procedure to produce Möbius iterated function systems on the unit disc.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.681-699
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• 2020

In this paper, topological entropy of iterated function systems (IFS) on one dimensional spaces is considered. Estimation of an upper bound of topological entropy of piecewise monotone IFS is obtained by open covers. Then, we provide a way to calculate topological entropy of piecewise monotone IFS. In the following, some examples are given to illustrate our theoretical results. Finally, we have a discussion about the possible applications of these examples in various sciences.

• 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.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.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.113-121
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• 2002

We construct lots of non-self similar fractal sets called generalized Markov attractors for a given (hyperbolic) iterated function system and calculated bounds of their Hausdorff dimensions.

• Journal of Korea Game Society
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• v.14 no.6
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• pp.109-118
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• 2014

We studied the creation of fractal images with polygonal rotation symmetry. As in Loocke's method[13] we start with IFS of affine functions that create polygonal fractals and extends the IFS by adding functions that create Julia sets instead of adding square root functions. The resulting images are rotationally symmetric and Julia set shaped. Also we can improve fractal images by modifying probabilistic IFS algorithm, and we suggest a method of deforming Julia set by changing exponent value.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.929-942
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• 2023

In this paper, we discuss topological ergodic shadowing property and topological pseudo-orbital specification property of iterated function systems(IFS) on uniform spaces. We show that an IFS on a sequentially compact uniform space with topological ergodic shadowing property has topological shadowing property. We define the notion of topological pseudo-orbital specification property and investigate its relation to topological ergodic shadowing property. We find that a topologically mixing IFS on a compact and sequentially compact uniform space with topological shadowing property has topological pseudo-orbital specification property and thus has topological ergodic shadowing property.

• Proceedings of the KOSOMBE Conference
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• v.1994 no.05
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• pp.43-48
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• 1994

본 논문은 반복 수축 변환의 프랙탈(fractal) 이론에 근거한 심전도 데이터 압축에 관한 연구이다. 심전도 데이터에 반복 함수계(Iterated Function System : IFS) 모델을 적용하여 신호 자체의 자기 유사성(self-similarity)을 반복 수축 변환으로 표현하고, 그 매개변수만을 저장한다. 재구성시는 변환 매개변수를 반복 적용하여 원래의 신호에 근사되어지는 값을 얻게 된다. 심전도 데이타는 부분적으로 자기 유사성을 갖는다고 보고, 부분 자기-유사 프랙탈 모델(piecewise self-affine fractal model)로 표현될 수 있다. 이 모델은 신호를 특정 구간들로 나누어 각 구간들에 대해 최적 프랙탈 보간(fractal interpolation)을 구하고 그 중 오차가 가장 작은 매개변수만을 추출하여 저장한다. 이 방법을 심전도 데이타에 적용한 결과 특정 압축율에 대해 아주 적은 재생오차 (percent root-mean-square difference : PRD)를 얻을 수 있었다.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.583-605
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• 2024

This paper discusses the properties of attractors of Type 1 IFS which construct self similar fractals on product spaces. General results like continuity theorem and Collage theorem for Type 1 IFS are established. An algebraic equivalent condition for the open set condition is studied to characterize the points outside a feasible open set. Connectedness properties of Type 1 IFS are mainly discussed. Equivalence condition for connectedness, arc wise connectedness and locally connectedness of a Type 1 IFS is established. A relation connecting separation properties and topological properties of Type 1 IFS attractors is studied using a generalized address system in product spaces. A construction of 3D fractal images is proposed as an application of the Type 1 IFS theory.