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Automorphisms of free groups have asymptotically periodic dynamics

Gilbert Levitt·Martin Lustig
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Abstract

We show that every automorphism $α$ of a free group $F_k$ of finite rank $k$ has {\it asymptotically periodic} dynamics on $F_k$ and its boundary $\partial F_k$: there exists a positive power $α^q$ such that every element of the compactum $F_k \cup \partial F_k$ converges to a fixed point under iteration of $α^q$.

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Gilbert Levitt, Martin Lustig. 2008-01-31. Automorphisms of free groups have asymptotically periodic dynamics. https://arxiv.org/abs/math/0407437

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