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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A Farey tree organization of locking regions for simple circle maps
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by K. M. Brucks and C. Tresser PDF
Proc. Amer. Math. Soc. 124 (1996), 637-647 Request permission


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:
  • C. Tresser
  • Affiliation: Thomas J. Watson Research Center, I.B.M., P.O. Box 218, Yorktown Heights, New York 10598
  • MR Author ID: 174225
  • Email:
  • Received by editor(s): July 20, 1994
  • Communicated by: Linda Keen
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 637-647
  • MSC (1991): Primary 58F03
  • DOI:
  • MathSciNet review: 1291764