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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Rotating an interval and a circle
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by Alexander Blokh and Michał Misiurewicz
Trans. Amer. Math. Soc. 351 (1999), 63-78
DOI: https://doi.org/10.1090/S0002-9947-99-02367-3
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Abstract:

We compare periodic orbits of circle rotations with their counterparts for interval maps. We prove that they are conjugate via a map of modality larger by at most 2 than the modality of the interval map. The proof is based on observation of trips of inhabitants of the Green Islands in the Black Sea.
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Bibliographic Information
  • Alexander Blokh
  • Affiliation: Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, Alabama 35294-2060
  • MR Author ID: 196866
  • Email: ablokh@math.uab.edu
  • Michał Misiurewicz
  • Affiliation: Department of Mathematical Sciences, IUPUI, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216
  • MR Author ID: 125475
  • Email: mmisiure@math.iupui.edu
  • Received by editor(s): August 26, 1996
  • Additional Notes: The first author was partially supported by the NSF grant DMS-9626303. The second author was partially supported by the NSF grant DMS-9305899
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 63-78
  • MSC (1991): Primary 54H20, 58F03, 58F08
  • DOI: https://doi.org/10.1090/S0002-9947-99-02367-3
  • MathSciNet review: 1621717