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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Minimal $C^1$-diffeomorphisms of the circle which admit measurable fundamental domains
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by Hiroki Kodama and Shigenori Matsumoto PDF
Proc. Amer. Math. Soc. 141 (2013), 2061-2067 Request permission

Abstract:

We construct, for each irrational number $\alpha$, a minimal $C^1$-diffeo- morphism of the circle with rotation number $\alpha$ which admits a measurable fundamental domain with respect to the Lebesgue measure.
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Additional Information
  • Hiroki Kodama
  • Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914 Japan
  • Email: kodama@ms.u-tokyo.ac.jp
  • Shigenori Matsumoto
  • Affiliation: Department of Mathematics, College of Science and Technology, Nihon University, 1-8-14 Kanda, Surugadai, Chiyoda-ku, Tokyo, 101-8308 Japan
  • MR Author ID: 214791
  • ORCID: 0000-0002-5851-7235
  • Email: matsumo@math.cst.nihon-u.ac.jp
  • Received by editor(s): June 24, 2011
  • Received by editor(s) in revised form: September 21, 2011, and October 2, 2011
  • Published electronically: January 15, 2013
  • Additional Notes: The first author was partially supported by the Japan Society for the Promotion of Science (JSPS) through its “Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program)”.
    The second author was partially supported by Grant-in-Aid for Scientific Research (C) No. 20540096
  • Communicated by: Bryna Kra
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 2061-2067
  • MSC (2010): Primary 37E15; Secondary 37C05, 37A40
  • DOI: https://doi.org/10.1090/S0002-9939-2013-11472-3
  • MathSciNet review: 3034431