FUJIKAWA, Ege

*The order of periodic elements of Teichmüller modular groups*

### Abstract

We consider
a quasiconformal automorphism of a Riemann surface,
which fixes the homotopy class of a simple closed geodesic.
Under certain conditions on the injectivity radius
of the surface and bounds on the dilatation of the map,
the automorphism induces a periodic element
of the Teichmüller modular group.
We may also estimate the order of the period.

submission: 19 October, 2003

revision: 13 October, 2004

to appear in Tohoku Math. J.

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