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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Rotating an interval and a circle


Authors: Alexander Blokh and Michal Misiurewicz
Journal: Trans. Amer. Math. Soc. 351 (1999), 63-78
MSC (1991): Primary 54H20, 58F03, 58F08
MathSciNet review: 1621717
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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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Additional Information

Alexander Blokh
Affiliation: Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, Alabama 35294-2060
Email: ablokh@math.uab.edu

Michal Misiurewicz
Affiliation: Department of Mathematical Sciences, IUPUI, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216
Email: mmisiure@math.iupui.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02367-3
PII: S 0002-9947(99)02367-3
Keywords: Periodic points, rotation numbers, interval maps
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
Article copyright: © Copyright 1999 American Mathematical Society