Abstract

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

Further results about the dynamics of α, as well as an extension from F_k to word-hyperbolic groups, are given in the later sections.