A formula for the fractal dimension d ∼ 0 . 87 of the Cantorian set underlying the Devil ’ s staircase associated with the Circle Map
نویسنده
چکیده
The Cantor set complementary to the Devil’s Staircase associated with the Circle Map has a fractal dimension d ∼ 0.87, universal for a wide range of maps, such results being of a numerical character. In this paper we deduce a formula for such dimensional value, the corresponding theoretical reasoning permits conjecturing on the nature of its universality. The Devil’s Staircase associated with the Circle Map is a function that transforms horizontal unit interval I onto I, and is endowed with the Farey-Brocot (F −B) structure in the vertical axis via the rational heights of stability intervals. The underlying Cantordust fractal set Ω in the horizontal axis, Ω ⊂ I, with fractal dimension 1 ar X iv :0 71 1. 27 06 v1 [ m at hph ] 1 7 N ov 2 00 7
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تاریخ انتشار 2008