• 대한수학회지
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• 제48권6호
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• pp.1143-1152
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• 2011

The existence of periodic solutions for the planar Hamiltonian systems with positively homogeneous Hamiltonian is discussed. The asymptotic expansion of the Poincar$\acute{e}$ map is calculated up to higher order and some sufficient conditions for the existence of periodic solutions are given in the case when the first order term of the Poincar$\acute{e}$ map is identically zero.

• 자연과학논문집
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• 제17권1호
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• pp.1-12
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• 2006

이 논문의 주된 결과는 Klein bottle상의 주기함수의 Per(f)를 Nielsen 수를 이용하여 구한 것이다.

• 대한수학회지
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• 제36권2호
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• pp.403-419
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• 1999

We introduce a Hamiltonian system which consists of two balls in the vertical line colliding elastically with each other and the floor. Wojtkowski proved that for the system of two linear balls with a linear potential (with gravity), there is a periodic orbit which becomes linearly stable if m1

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1997년도 추계학술대회논문집; 한국과학기술회관; 6 Nov. 1997
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• pp.154-159
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• 1997

In this paper, we describe the OGY method that convert the motion on a chaotic attractor to attracting time periodic motion by malting only small perturbations of a control parameter. The OGY method is illustrated by application to the control of the chaotic motion in chaotic attractor to happen at the famous Logistic map and Henon map and confirm it by making periodic motion. We apply it the chaotic motion at the behavior of the thin beam under periodic torsional base-excitation, and this chaotic motion is made the periodic motion by numerical experiment in the time evaluation on this chaotic motion. We apply the OGY method with the Jacobian matrix to control the chaotic motion to the periodic motion.

• 한국항행학회논문지
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• 제26권6호
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• pp.474-480
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• 2022

광 위상 공액은 파장 분할 다중 (WDM; wavelength division multiplexed) 신호의 장거리 전송을 위해 필수적인 색 분산과 비선형성에 의한 왜곡을 보상할 수 있는 기술 중 하나이다. 이 기술이 그동안 가지고 있었던 한계를 주기적 분산 프로파일을 갖는 분산 맵을 통해 해소하는 방안을 제안하고 분석해 보았다. 제안하는 시스템에서 광 위상 공액기 (OPC; optical phase conjugator)는 전체 링크의 1:2 또는 2:1의 위치에 배치되고, 분산 맵의 프로파일은 사인파 또는 반전된 사인파 모양의 주기적 형태를 갖는다. OPC가 전체 링크의 2:1 지점이 아닌 1:2 지점에 위치할 때 제안된 주기적 형태의 분산 맵을 통해 왜곡된 960 Gb/s WDM 신호의 보상이 더욱 개선되는 것을 확인하였다. 또한 제안된 주기적 분산 맵을 갖는 분산 제어 링크의 설계 융통성을 늘리기 위해서는 중계 구간에 할당되는 최대 RDPS (residual dispersion per span)가 1,800 ps/nm 이상이 되어야 하는 것도 알 수 있었다.

• 충청수학회지
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• 제20권4호
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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.

• 대한수학회논문집
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• 제12권3호
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• pp.779-788
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• 1997

In this work, using the exact separatrix map which provides an efficient way to describe dynamics near the separatrix, we study the stochastic layer near the separatrix of a one-degree-of-freedom Hamilitonian system with time periodic perturbation. Applying the twist map theory to the exact separatrix map, T. Ahn, G. I. Kim and S. Kim proved the existence of the uniformly hyperbolic invariant set(UHIS) near separatrix. Using the theorems of Bowen and Franks, we prove this UHIS has measure zero.

• 대한수학회보
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• 제61권1호
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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.

• 충청수학회지
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• 제13권2호
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• pp.1-7
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• 2001

In this paper, we show that for a homotopically periodic (i.e., $fk{\simeq}id$, for some $k{\geq}1$) self map f of a Seifert 3-manifold with $P{\widetilde{SL(2,}}\mathbb{R})$-geometry, N(f) = L(f) = 0.

• East Asian mathematical journal
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• 제30권5호
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• pp.583-597
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• 2014

In this paper, we study an area-preserving piecewise linear map with the feature of dangerous border collision bifurcations. Using this map, we study dynamical properties occurred in the invariant set, specially related to the boundary of KAM-tori, and the existence and stabilities of periodic orbits. The result shows that elliptic regions having periodic orbits and chaotic region can be divided by smooth curve, which is an unexpected result occurred in area preserving smooth dynamical systems.