• 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.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.759-764
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• 2004

Let X = {a} ${\cup}$ {$a_{i}$ ${$\mid$}$i $\in$ N} be a subspace of Euclidean space $E^2$ such that $lim_{{i}{\longrightarrow}{$\infty}}a_{i}$ = a and $a_{i}\;{\neq}\;a_{j}$ for $i{\neq}j$. Then it is well known that the space X has no expansive homeomorphisms with the shadowing property. In this paper we show that the set of all expansive homeomorphisms with the shadowing property on the space Y is dense in the space H(Y) of all homeomorphisms on Y, where Y = {a, b} ${\cup}$ {$a_{i}{$\mid$}i{\in}Z$} is a subspace of $E^2$ such that $lim_{i}$-$\infty$ $a_{i}$ = b and $lim_{{i}{\longrightarrow}{$\infty}}a_{i}$ = a with the following properties; $a_{i}{\neq}a_{j}$ for $i{\neq}j$ and $a{\neq}b$.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.9
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• pp.64-74
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• 2003

This paper proposes a new autonomous stationkeeping system suitable for geostationary satellite and conducts computer simulation to verify the proposed algorithm. The proposed onboard system receives pseudo-range signal from ground equipments located at two different position with long baseline, determines the orbit error in realtime and generates orbit control commands. For minimized onboard stationkeeping logic and better reliability, the orbit controller is designed to generate control signal to have the orbit roughly follow predetermined reference range data which is generated through ground based computer simulation. The reference range data is assumed to be uploaded with time tag. A simple orbit controller is proposed which combines the reference $\Delta$V and feedback control signal. Finally, the performance of the proposed system is verified through the computer simulations.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.411-418
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• 2009

In this paper we introduce the notions of strict persistence and weakly strict persistence which are stronger than those of persistence and weak persistence, respectively, and study their relations with shadowing property. In particular, we show that the weakly strict persistence and the weak inverse shadowing property are locally generic in Z(M).

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.645-650
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• 2008

Let M be a generalized homogeneous compact space, and let Z(M) denotes the space of homeomorphisms of M with the $C^0$ topology. In this paper, we show that if the interior of the set of weak stable homeomorphisms on M is not empty then for any open subset W of Z(M) containing only weak stable homeomorphisms the orbital shadowing property is generic in W.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.10
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• pp.67-76
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• 2004

This paper improves existing 'fly-the-wire' based autonomous station-keeping system, suitable for geostationary satellite and introduces results of computer simulations conducted to verify the algorithm. The on-board stationkeeping system receives pseudo-range signals from two ground equipments located with long baseline, determines the orbit error in realtime and generates orbit control commands. To reduce fuel consumption, this paper proposes an on-board orbit control logic using modified fly-the-wire method. The modified fly-the-wire method de-couples error components into two dynamic modes, harmonic and linear motion. The harmonic error components are removed by applying output commands produced by feedback controller, and the linear motions are controlled by the correction ${\Delta}V\;s$ added to reference maneuvers. The reference maneuvers are generated through the ground based computer simulation and embedded or uploaded into the on-board computer with time tags. Finally, the performance of the proposed algorithm is verified through a series of computer simulations.