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Connectedness of the Arnold tongues for double standard maps
Author(s):
Alexandre
Dezotti
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3569-3583.
MSC (2010):
Primary 37E10, 37F45;
Secondary 37F30, 37C15, 37C05
Posted:
April 7, 2010
MathSciNet review:
2661556
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Abstract:
We show that Arnold tongues for the family of double standard maps 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  , has only one critical orbit taking symmetry into account.
References:
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Blaschke products of degree 4 and cubic polynomials. In preparation. - 4.
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On the tip of the tongue.
J. Fixed Point Theory Appl., 3(1):131-141, 2008. MR 2402913 (2009g:37037) - 6.
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To appear in Duke Math. Journal, 2009.
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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:
10.1090/S0002-9939-10-10355-4
PII:
S 0002-9939(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
Posted:
April 7, 2010
Communicated by:
Bryna Kra
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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