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Connectedness of the Arnold tongues for double standard maps


Author: Alexandre Dezotti
Journal: Proc. Amer. Math. Soc. 138 (2010), 3569-3583
MSC (2010): Primary 37E10, 37F45; Secondary 37F30, 37C15, 37C05
DOI: https://doi.org/10.1090/S0002-9939-10-10355-4
Published electronically: April 7, 2010
MathSciNet review: 2661556
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that Arnold tongues for the family of double standard maps

$\displaystyle f_{a,b}(x)=2x+a-(b/\pi)sin(2 \pi x)$

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 orbit taking symmetry into account.


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Additional Information

Alexandre Dezotti
Affiliation: Institut de mathématiques de Toulouse UMR5219, Université de Toulouse, UPS, 118, route de Narbonne, 31062 Toulouse Cedex, France
Email: dezotti@math.univ-toulouse.fr

DOI: https://doi.org/10.1090/S0002-9939-10-10355-4
Received by editor(s): July 4, 2009
Received by editor(s) in revised form: September 17, 2009, September 29, 2009, December 22, 2009, December 23, 2009, and December 26, 2009
Published electronically: April 7, 2010
Communicated by: Bryna Kra
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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