Connectedness of the Arnold Tongues for Double Standard Maps
نویسنده
چکیده
We show that Arnold tongues for the family of double standard maps fa,b(x) = 2x+ a− (b/π)sin(2πx) are connected. This proof is accomplished in the complex domain by means of quasiconformal techniques and depends partly upon the fact that the complexification of fa,b, has only one critical orbit taking symmetry into account.
منابع مشابه
On the tip of the tongue . . .
Recently we investigated the family of double standard maps of the circle onto itself, given by fa,b(x) = 2x + a + b π sin(2πx) (mod 1). Similarly to the family of Arnold standard maps of the circle, Aa,b(x) = x + a + b 2π sin(2πx) (mod 1), if 0 < b ≤ 1 then any such map has at most one attracting periodic orbit. The values of the parameters for which such orbit exists are grouped into Arnold t...
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تاریخ انتشار 2009