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Proceedings of the American Mathematical Society

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A Farey tree organization of locking regions
for simple circle maps


Authors: K. M. Brucks and C. Tresser
Journal: Proc. Amer. Math. Soc. 124 (1996), 637-647
MSC (1991): Primary 58F03
DOI: https://doi.org/10.1090/S0002-9939-96-03025-0
MathSciNet review: 1291764
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $f$ be a $C^3$ circle endomorphism of degree one with exactly two critical points and negative Schwarzian derivative. Assume that there is no real number $a$ such that $f + a$ has a unique rotation number equal to $\frac{p}{q}$. Then the same holds true for any $\frac{p'}{q'}$ such that $\frac{p}{q}$ stands above $\frac{p'}{q'}$ in the Farey tree and can be related to it by a path on the tree.


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Additional Information

K. M. Brucks
Affiliation: Department of Mathematical Sciences, University of Wisconsin, Milwaukee, Wisconsin 53211
Email: kmbrucks@csd.uwm.edu

C. Tresser
Affiliation: Thomas J. Watson Research Center, I.B.M., P.O. Box 218, Yorktown Heights, New York 10598
Email: tresser@watson.ibm.com

DOI: https://doi.org/10.1090/S0002-9939-96-03025-0
Received by editor(s): July 20, 1994
Communicated by: Linda Keen
Article copyright: © Copyright 1996 American Mathematical Society