A concrete family of automorphisms αn of the free group Fn
is exhibited, for any n ≥ 3, and the following properties are
proved: αn is irreducible with irreducible powers, has
trivial fixed subgroup, and has 2n-1 attractive as well as 2n
repelling fixed points at ∂Fn.
As a consequence of a recent result of V Guirardel there can not be
more fixed points on ∂Fn, so that this family provides the
answer to a question posed by G Levitt.
