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

By Gilbert Levitt, Martin Lustig. Journal of the Institute of Mathematics of Jussieu, 2003

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The actions of ${\mathit{Out}(F_k)}$ on the boundary of Outer space and on the space of currents: minimal sets and equivariant incompatibility (2006, background): “Levitt and Lustig [ 25 ] proved that such automorphisms have “North-South” dynamics on @CV (F) (and indeed on the entire space CV (F)) and hence, clearly, their attracting fixed points must belong to MCV . It is also known that”
Automorphism groups of free groups, surface groups and free abelian groups (2005, background): “in the natural boundary of the symmetric space analog), and the action of the cyclic subgroup generated by the element exhibits the north-south dynamics familiar from the action of hyperbolic matrices on the closure of the Poincar´e disc [ 62 ], [54].”
Axes in Outer Space (2006, unknown): “…infinity: loxodromic isometries of H n ; pseudo-Anosov mapping classes of a surface [McC85]; and outer automorphisms of F r which are fully irreducible [LL03], meaning that no proper, nontrivial free factor of F r has a conjugacy class which is periodic under the action of the outer automorphism.”