Camille Horbez, University of Paris-Sud

Growth under automorphisms of hyperbolic groups

Let G be a finitely generated group, let S be a finite generating set of G, and let f be an automorphism of G. A natural question is the following: what are the possible asymptotic behaviours for the length of f^n(g) written as a word in the generating set S, as n goes to infinity, and as g varies in the group G? Growth was described by Thurston when G is the fundamental group of a hyperbolic surface, and can be understood from Bestvina-Handel's work on train-tracks when G is a free group. We investigate the case of a general torsion-free hyperbolic group. This is a joint work with Rémi Coulon, Arnaud Hilion, and Gilbert Levitt.