Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A Farey tree organization of locking regions for simple circle maps

Author(s): K. M. Brucks; C. Tresser
Journal: Proc. Amer. Math. Soc. 124 (1996), 637-647.
MSC (1991): Primary 58F03
MathSciNet review: 1291764
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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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