Mathematics – Dynamical Systems
Scientific paper
2008-08-18
Mathematics
Dynamical Systems
5 pages
Scientific paper
We consider the group of smooth diffeomorphisms of the circle. We show that
any recurrent $f$ (in the sense that $\{f^n\}_{n \in Z}$ is not discrete) is in
fact a distortion element (in the sense that its iterates can be written as
short compositions involving finitely many smooth diffeomorphisms). Thus
rotations are distortion elements.
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