Generic hamiltonian systems often exhibit slow dynamics. The origin of the slow behavior is thought to be from the stagnant motion in the neighborhood of the outermost Kolmogorov-Arnold-Moser (KAM) tori. We investigate the onset mechanism of such slow dynamics by using a mushroom billiard with a dielectric medium. Bifurcation processes are precisely studied in the vicinity of the outermost KAM tori when the refraction index of the dielectric medium is changed smoothly, and it is shown that the stagnant motion is generated near singular points in the chaotic sea. There are two types of stagnant aspects coexisting in the generic case, for which the distributions of the escape time of stagnant motion are theoretically determined.
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