• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.727-730
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• 2013

We prove an inequality between topological entropy and asymptotical growth of periodic orbits for $C^1$ generic diffeomorphisms.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.155-158
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• 1997

In this paper, we present new results concerning the relationship between the input-output and Lyapunov stability of nonlinear system possessing a periodic orbit. Definition of small-signal finite-gain L$\sub$p/ stability around periodic orbit is introduced. We show L$\sub$p/ stability of exponentially stable periodic orbit using quadratic Lyapunov functions for the periodic orbit. The L$\sub$2/ gain analysis is presented with Hamiltonian-Jacobi inequality along with an example.

• Journal of Astronomy and Space Sciences
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• v.5 no.2
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• pp.129-141
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• 1988

Using the numerical solution in the plane restricted problem of three bodies, abut 490 periodic orbits are computed numerically around the $L_5$ of Sun-Jupiter and about 1600 periodic orbits also be done around the $L_5$ of Sun-Jupiter system. But, in Earth-Moon system, the complex shapes and dents appear around the $L_5$ and periodic orbits intersect one another in the place where dents are shown. And there is a region that three different periodic orbits exist with the same period in this system. The increase of energy is in inverse proportion to that of period in the part of this region. The regions can exist around the $L_5$ of Sun-Jupiter system where periodic orbit can be unstable by perturbation of other force besides the gravitational force of Jupiter. These regions which is close to $L_5$ are a~5.12 AU. The Trojan asteroids that have a small eccentricity and inclination can not exist in this region.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.193-209
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• 2006

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. In this paper, extending Cardona and Wong's work on relative Reidemeister numbers, we show that the Reidemeister orbit numbers can be used to calculate the relative essential orbit numbers. We also apply the relative Reidemeister orbit number to study periodic orbits of fibre preserving maps.

• Journal of The Korean Astronomical Society
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• v.29 no.spc1
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• pp.443-444
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• 1996

From 146 B.C. to A.D. 1760, 363 sets of cometary observations have been recorded in Chinese Ancient Records of Celestial Phenomena. The positions of all recorded comets, or their paths, on the sky are compared. Taking into account the perturbations of all nine planets and using the numerical method of N-body problem, the orbits of well-recorded comets are calculated. Identification of a periodic comet is presented.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1229-1254
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• 2022

In this paper, we introduce the concepts of (quasi-)weakly almost periodic point and minimal center of attraction for ℤ^d₊-actions, explore the connections of levels of the topological structure the orbits of (quasi-)weakly almost periodic points and discuss the relations between (quasi-)weakly almost periodic point and minimal center of attraction. Especially, we investigate the chaotic dynamics near or inside the minimal center of attraction of a point in the cases of S-generic setting and non S-generic setting, respectively. Actually, we show that weakly almost periodic points and quasi-weakly almost periodic points have distinct topological structures of the orbits and we prove that if the minimal center of attraction of a point is non S-generic, then there exist certain Li-Yorke chaotic properties inside the involved minimal center of attraction and sensitivity near the involved minimal center of attraction; if the minimal center of attraction of a point is S-generic, then there exist stronger Li-Yorke chaotic (Auslander-Yorke chaotic) dynamics and sensitivity (ℵ₀-sensitivity) in the involved minimal center of attraction.

• Journal of computational fluids engineering
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• v.20 no.4
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• pp.58-62
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• 2015

Recent studies on wall-bounded shear flow have emphasized the significance of the stable manifold of simple nonlinear invariant solutions to the Navier-Stokes equation in the formation of the boundary between the laminar and turbulent regions in state space. In this paper we present newly discovered homoclinic orbits of the Kawahara and Kida(2001) periodic solution in plane Couette flow. We show that as the Reynolds number decreases a pair of homoclinic orbits move closer to each other until they disappear to exhibit homoclinic tangency.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.1
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• pp.81.1-81.1
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• 2014

Kepler-47 is the first multi-body circumbinary planetary system detected by the Kepler space telescope. The two planets were detected by the transit method. In the discovery paper the authors report about the presence of an additional transit-like signal in their dataset which cannot be explained by a four-body (binary + 2 planets) system. Therefore it is likely that the unexplained signal could be due to a third planet. In this talk I will present recent results from a dynamical investigation of the five-body system (binary + 3 planets). We have applied the MEGNO technique to detect regions of quasi- or near quasi-periodic orbits of a hypothetical third planet. Quasi-periodic regions exists for a third planet and the long-term stability has been tested. Although the existence of a third planet is most likely to be confirmed from transit photometry we calculate transit-timing variation (TTV) signals due to the third planet which also can be used to infer its presence.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.857-870
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• 2000

In this paper, we estimate correlation dimensions of discrete quasi periodic ordits with frequencies, irrational numbers, which are called quasi Roth numbers. We specify the lower estimate valuse of the dimensions by using the parameters which are derived the rational approximable properties of the quasi Roth numbers.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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• pp.113-121
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• 2003

This paper is concerned with some properties of stable domains and limit functions. Using the relationship between cycles of periodic stable domains and orbits of critical points and using the Sullivan theorem [19], we prove that the value of a constant limit function in some stable domain for a rational function f of degree at least two lies in the closure of the set of critical orbits of f.