Minimal $C^1$-diffeomorphisms of the circle which admit measurable fundamental domains
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- by Hiroki Kodama and Shigenori Matsumoto
- Proc. Amer. Math. Soc. 141 (2013), 2061-2067
- DOI: https://doi.org/10.1090/S0002-9939-2013-11472-3
- Published electronically: January 15, 2013
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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.References
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Bibliographic 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 âFunding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program)â.
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