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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Minimal $ C^1$-diffeomorphisms of the circle which admit measurable fundamental domains


Authors: Hiroki Kodama and Shigenori Matsumoto
Journal: Proc. Amer. Math. Soc. 141 (2013), 2061-2067
MSC (2010): Primary 37E15; Secondary 37C05, 37A40
Published electronically: January 15, 2013
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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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
Email: matsumo@math.cst.nihon-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11472-3
PII: S 0002-9939(2013)11472-3
Keywords: Diffeomorphism, minimality, rotation number, ergodicity
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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.