Connectedness of the Arnold Tongues for Double Standard Maps

Abstract

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. 

Topics

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Cite this paper

@inproceedings{Dezotti2009ConnectednessOT, title={Connectedness of the Arnold Tongues for Double Standard Maps}, author={Alexandre Dezotti}, year={2009} }