Automorphisms of free groups have asymptotically periodic dynamics

Abstract

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 ${\alpha }^q$.

Final version. To appear in Crelle's journal