Automorphisms of free groups have asymptotically periodic dynamics

Details Automorphisms of free groups have asymptotically periodic dynamics Automorphisms of free groups have asymptotically periodic dynamics

2004-07-26

arxiv.org/abs/math/0407437v2

J. reine angew. Math 619 (2008), 1-36

Mathematics

Group Theory

Final version. To appear in Crelle's journal

Scientific paper

We show that every automorphism $\alpha$ 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 $\alpha^q$ such that every
element of the compactum $F_k \cup \partial F_k$ converges to a fixed point
under iteration of $\alpha^q$.

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