Dynamics of fully irreducible automorphisms of free products

Abstract

Let G be a free product and $\mathrm{Out}\left(G\right)$ the outer automorphism group of G. In this article using the theory of laminations we give a criterion for a subgroup H of $\mathrm{Out}\left(G\right)$ to contain a nonabelian free subgroup. We also study the centraliser of a fully irreducible element of $\mathrm{Out}\left(G\right)$ and the stabiliser of its associated lamination.