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arXiv · 0808.2334

Distortion elements in $Diff^\infty(R/Z)$

Artur Avila
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Abstract

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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Artur Avila. 2008-08-18. Distortion elements in $Diff^\infty(R/Z)$. https://arxiv.org/abs/0808.2334

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