Connectedness of the Arnold tongues for double standard maps

Details Connectedness of the Arnold tongues for double standard maps Connectedness of the Arnold tongues for double standard maps

2009-04-03

arxiv.org/abs/0904.0593v2

Mathematics

Dynamical Systems

12 pages, 4 figures, translated in english

Scientific paper

We show that the Arnold tongues of the family of double standard maps
f_{a,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 f_{a,b} has only one
critical point taking symmetry into account.

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