Advanced Studies in Pure Mathematics

Rotation number and lifts of a Fuchsian action of the modular group on the circle

Yoshifumi Matsuda

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Abstract

We characterize the semi-conjugacy class of a Fuchsian action of the modular group on the circle in terms of rotation numbers of two standard generators and that of their product. We also show that among lifts of a Fuchsian action of the modular group, only 5-fold lift admits a similar characterization. These results indicate similarity and difference between rotation number and linear character.

Article information

Source
Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, T. Asuke, S. Matsumoto and Y. Mitsumatsu, eds. (Tokyo: Mathematical Society of Japan, 2017), 429-440

Dates
Received: 18 August 2014
Revised: 1 December 2014
First available in Project Euclid: 4 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538671779

Digital Object Identifier
doi:10.2969/aspm/07210429

Mathematical Reviews number (MathSciNet)
MR3726722

Zentralblatt MATH identifier
1385.37060

Subjects
Primary: 37E45: Rotation numbers and vectors
Secondary: 37C85: Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx] 37E10: Maps of the circle

Keywords
Rotation number modular group group actions on the circle

Citation

Matsuda, Yoshifumi. Rotation number and lifts of a Fuchsian action of the modular group on the circle. Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, 429--440, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07210429. https://projecteuclid.org/euclid.aspm/1538671779


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