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

Matsuda, Yoshifumi

doi:10.2969/aspm/07210429

VOL. 72 | 2017 Rotation number and lifts of a Fuchsian action of the modular group on the circle

Yoshifumi Matsuda

Editor(s) Taro Asuke, Shigenori Matsumoto, Yoshihiko Mitsumatsu

Adv. Stud. Pure Math., 2017: 429-440 (2017) DOI: 10.2969/aspm/07210429

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.