Dynamics of free group automorphisms

2003/08/20 by Peter Brinkmann, Brinkmann, Peter
Mathematics · #37E30 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:37E30

paper · pdf · doi:10.48550/arxiv.math/0308199

35 pages, 6 figures; updated to reflect arXiv:0806.2889v1 in particular

arxiv created 2008/06/17 · arxiv updated 2009/12/01

Abstract

We present a coarse convexity result for the dynamics of free group automorphisms: Given an automorphism ϕ of a finitely generated free group F, we show that for all x∈ F and 0≤ i≤ N, the length of ϕⁱ(x) is bounded above by a constant multiple of the sum of the lengths of x and ϕ^N(x), with the constant depending only on ϕ.

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