• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.243-256
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• 2023

We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin [54]. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism f of a compact smooth manifold M has the robustly pointwise inverse pseudoorbit tracing property, f is structurally stable. (ii) For a C1 generic diffeomorphism f of a compact smooth manifold M, if f has the pointwise inverse pseudo-orbit tracing property, f is structurally stable. (iii) If a diffeomorphism f has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set Λ, then Λ is hyperbolic for f. Finally, (iv) for C¹ generically, if a diffeomorphism f has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set Λ, then Λ is hyperbolic for f. In addition, we investigate cases of volume preserving diffeomorphisms.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.287-292
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• 2020

In this paper, we prove that a distal homeomorphism f of a compact connected metric space X does not have the eventual pseudo orbit tracing property.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.343-348
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• 2007

In this paper, we show that if a homeomorphism has the pseudo-orbit-tracing-property and its nonwandering set is locally connected, then the limit sets of wandering points whose stable sets have nonempty interior consist of single periodic orbit.

• Journal of The Korean Astronomical Society
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• v.51 no.1
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• pp.1-4
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• 2018

We study the pseudo-synchronous orbital motion of a binary system on the main sequence. The equations of the pseudo-synchronous orbit are derived up to $O(e^4)$ where e is the eccentricy of the orbit. We integrate the equations to present their solutions. The theoretical results are applied to the evolution of the orbit and spin of the binary star Y Cygni, which has a current eccentricity of $e_0\;=\;0.142$. We tabulate our numerical results for the evolution of the orbit and spin per century. The numerical results for the semi-major axes and rotational angular velocities in the evolutional time scales of three stages (synchronization, circularization, and collapse time scale) are also tabulated. Synchronization is achieved in about $5{\times}10^3\;years$ followed by circularization lasting about $1{\times}10^5\;years$ before decaying in $2{\times}10^5\;years$.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.133-146
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• 2021

For pseudo-free and recurrent self-similar groups, we show that continuous orbit equivalence of inverse semigroup partial actions implies continuous orbit equivalence of group actions. Conversely, if group actions are continuous orbit equivalent, and the induced homeomorphism commutes with the shift maps on their groupoids, we obtain continuous orbit equivalence of inverse semigroup partial actions.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.871-878
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• 2010

In this paper, we show that if a homeomorphism has the pseudo-orbit-tracing-property and its nonwandering set is locally connected, then the points whose stable sets have nonempty interior are periodic points.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.42 no.3
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• pp.270-278
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• 2014

This paper describes an improvement of space objects orbit prediction. To screen possible collisions between operational satellites and space objects, the TLE (Two-Line Element) was used as pseudo-measurement and than the orbit determination and orbit prediction were performed through the flight dynamics system. For determining the orbits, the state vectors were assumed by a series of TLEs within a certain period. The propagation error was analyzed according to the fitting period and a number of pseudo-observations. In order to find out the improvement of orbit prediction with the proposed method, KOMPSAT-2, 3 having the precise orbit in the meter-level range were first applied. Then the result applied to space objects under the same conditions was analyzed. As a result of the RMS error comparison with the orbit prediction of space object, the precision of orbit prediction was improved by approximately 90% for seven days prediction. The improved orbit prediction of space objects can be utilized in the daily analysis for initial screening of the close space objects at high risk.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.2325-2330
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• 2003

GPS based orbit determination system for the KOMPSAT-2 has been developed. Two types of orbit determination software such as operational orbit determination and precise orbit determination are designed and implemented. GPS navigation solutions from on-board the satellite are used for the operational orbit determination and raw measurements data such as C/A code pseudo-range and L1 carrier phase for the precise orbit determination. Operational concept, architectural design, software implementation, and performance test are described.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.355-361
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• 2006

We prove that if a continuous surjective map f on a compact metric space X has the average shadowing property, then every point x is chain recurrent. We also show that if a homeomorphism f has more than two fixed points on $S^1$, then f does not satisfy the average shadowing property. Moreover, we construct a homeomorphism on a circle which satisfies the shadowing property but not the average shadowing property. This shows that the converse of the theorem 1.1 in [6] is not true.

• 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).