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We show that the Arnold tongues of the family of double standard mapsf_{a,b}(x) = 2x + a + (b/pi) sin(2 pi x), are connected. This proof isaccomplished in the complex domain by means of quasiconformal techniques anddepends partly upon the fact that the complexification of f_{a,b} has only onecritical point taking symmetry into account.

Connectedness of the Arnold tongues for double standard maps