Connectedness of the Arnold tongues for double standard maps
Abstract
We show that the Arnold tongues of the family of double standard maps fa,b(x) = 2x + a + (b/pi) sin(2 pi x), 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 point taking symmetry into account.
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