IRREDUCIBLE AUTOMORPHISMS OF $F_{n}$ HAVE NORTH–SOUTH DYNAMICS ON COMPACTIFIED OUTER SPACE

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Abstract
We show that if an automorphism of a non-abelian free group is irreducible with irreducible powers, it acts on the boundary of Culler–Vogtmann’s outer space with north–south dynamics: there are two fixed points, one attracting and one repelling, and orbits accumulate only on these points. The main new tool we use is the equivariant assignment of a point with trivial arc stabilizers; this point , or in its metric completion, or in its boundary.AMS 2000 Mathematics subject classification: Primary 20F65; 20E05; 20E08