Connectedness of the Arnold tongues for double standard maps
Dynamical Systems
2009-09-01 v2 Complex Variables
Abstract
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.
Cite
@article{arxiv.0904.0593,
title = {Connectedness of the Arnold tongues for double standard maps},
author = {Alexandre Dezotti},
journal= {arXiv preprint arXiv:0904.0593},
year = {2009}
}
Comments
12 pages, 4 figures, translated in english