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Proceedings of the American Mathematical Society

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

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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

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
  • MR Author ID: 174225
  • Email: tresser@watson.ibm.com
  • 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: https://doi.org/10.1090/S0002-9939-96-03025-0
  • MathSciNet review: 1291764