Dynamics of free group automorphisms

Abstract

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

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

References in corpus (2)

• The Tits alternative for Out(F_n) I: Dynamics of exponentially-growing automorphisms
• The quadratic isoperimetric inequality for mapping tori of free group automorphisms I: Positive automorphisms

Cited by in corpus (1)

• Detecting automorphic orbits in free groups