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The smoothness of KAM (Kolmogorov-Arnold-Moser) curves when approaching the critical point which constitutes the existence/non-existence boundary of a KAM curve is investigated in the standard mapping as a typical example of analytical twist mappings. We give numerical results indicating that the KAM curve at the critical point is C1, but its derivative is not a function of bounded variation. The fractal distribution function of mapped points on such KAM curves is caused by this unbounded variation.
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Yamaguchi et al. (1999) studied this question.
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