Automorphisms of Free Groups Have Asymptotically Periodic Dynamics
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چکیده
We show that every automorphism α of a free group Fk of finite rank k has asymptotically periodic dynamics on Fk and its boundary ∂Fk: there exists a positive power α such that every element of the compactum Fk ∪ ∂Fk converges to a fixed point under iteration of α . Further results about the dynamics of α as well as an extension from Fk to word-hyperbolic groups are given in the later sections.
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تاریخ انتشار 2008