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Dynamics of free group automorphisms

Peter Brinkmann
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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 $x\in F$ and $0\leq i\leq N$, the length of $ϕ^i(x)$ 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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Peter Brinkmann. 2008-06-17. Dynamics of free group automorphisms. https://arxiv.org/abs/math/0308199

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