Dynamics of free group automorphisms

Details Dynamics of free group automorphisms Dynamics of free group automorphisms

2003-08-20

arxiv.org/abs/math/0308199v2

Mathematics

Group Theory

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

Scientific paper

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

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