Growth of intersection numbers for free group automorphisms

Jason Behrstock, Mladen Bestvina, Matt Clay

Published 2008-06-30, updated 2009-04-27Version 3

For a fully irreducible automorphism \phi of the free group F_k we compute the asymptotics of the intersection number n \mapsto i(T,T'\phi^n) for trees T,T' in Outer space. We also obtain qualitative information about the geometry of the Guirardel core for the trees T and T'\phi^n for n large.