# Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number function

Yoshifumi Matsuda^{[1]}

- [1] University of Tokyo Graduate School of Mathematical Sciences 3-8-1 Komaba Meguro Tokyo 153-8914 (Japan)

Annales de l’institut Fourier (2009)

- Volume: 59, Issue: 5, page 1819-1845
- ISSN: 0373-0956

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topMatsuda, Yoshifumi. "Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number function." Annales de l’institut Fourier 59.5 (2009): 1819-1845. <http://eudml.org/doc/10441>.

@article{Matsuda2009,

abstract = {We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the $C^1$-topology then it has a finite orbit. As a corollary, we show that if such a group has no finite orbit then each of its subgroups contains either a cyclic subgroup of finite index or a nonabelian free subgroup.},

affiliation = {University of Tokyo Graduate School of Mathematical Sciences 3-8-1 Komaba Meguro Tokyo 153-8914 (Japan)},

author = {Matsuda, Yoshifumi},

journal = {Annales de l’institut Fourier},

keywords = {Rotation number; circle diffeomorphisms; groups; local vector fields; Poincaré rotation number},

language = {eng},

number = {5},

pages = {1819-1845},

publisher = {Association des Annales de l’institut Fourier},

title = {Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number function},

url = {http://eudml.org/doc/10441},

volume = {59},

year = {2009},

}

TY - JOUR

AU - Matsuda, Yoshifumi

TI - Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number function

JO - Annales de l’institut Fourier

PY - 2009

PB - Association des Annales de l’institut Fourier

VL - 59

IS - 5

SP - 1819

EP - 1845

AB - We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the $C^1$-topology then it has a finite orbit. As a corollary, we show that if such a group has no finite orbit then each of its subgroups contains either a cyclic subgroup of finite index or a nonabelian free subgroup.

LA - eng

KW - Rotation number; circle diffeomorphisms; groups; local vector fields; Poincaré rotation number

UR - http://eudml.org/doc/10441

ER -

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