Connectedness of the Arnold tongues for double standard maps
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- by Alexandre Dezotti PDF
- Proc. Amer. Math. Soc. 138 (2010), 3569-3583 Request permission
Abstract:
We show that Arnold tongues for 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 orbit taking symmetry into account.References
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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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2661556