• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.147-159
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• 1999

Tabanov investigated the global symmetric perturbation of the integrable billiard mapping in the ellipse [3]. He showed the nonintegrability of the Birkhoff billiard in the perturbed domain by proving that the principal separatrices splitting angle is not zero.In this paper, using the exact separatrix map of an one-degree-of freedom Hamiltoniam system with time periodic perturbation, we show the existence the stochastic layer including the uniformly hyperbolic invariant set which implies the nonintegrability near the separatrices of a Birkhoff's billiard in the domain bounded by $C^2$ convex simple curve constructed by the generic global perturbation of the ellipse.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.50.3-50.3
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• 2019

The EUV wave is a disturbance that has been believed to be the fast-mode (shock) wave, which can propagate passing through magnetic field lines. After the passage of EUV waves, coronal streamers start to show kink-mode oscillations, and the footpoints, i.e., magnetic separatrices, of the oscillating streamers are observed as the so-called stationary front. We compare the stationary front observed by EUV imagers and coronal streamers observed in coronagraphic images. We analyze the successive events occurred in September 2011. We find that the stationary fronts are consistent with the coronal streamer boundaries, and they are located along the boundaries of coronal holes and active regions. Our results confirm that EUV waves are in fact fast-mode waves and demonstrate that the stationary front is a promising tool to probe into the source of slow solar wind that is the boundary of coronal streamers on the solar surface.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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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.