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Automorphisms of free groups have asymptotically periodic dynamics

Automorphisms of free groups have asymptotically periodic dynamics We show that every automorphism α of a free group F k of finite rank k has asymptotically periodic dynamics on F k and its boundary ∂ F k : there exists a positive power α q such that every element of the compactum converges to a fixed point under iteration of α q . Further results about the dynamics of α, as well as an extension from F k to word-hyperbolic groups, are given in the later sections. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal für die reine und angewandte Mathematik (Crelle's Journal) de Gruyter

Automorphisms of free groups have asymptotically periodic dynamics

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Publisher
de Gruyter
Copyright
© Walter de Gruyter Berlin · New York 2008
ISSN
0075-4102
eISSN
1435-5345
DOI
10.1515/CRELLE.2008.038
Publisher site
See Article on Publisher Site

Abstract

We show that every automorphism α of a free group F k of finite rank k has asymptotically periodic dynamics on F k and its boundary ∂ F k : there exists a positive power α q such that every element of the compactum converges to a fixed point under iteration of α q . Further results about the dynamics of α, as well as an extension from F k to word-hyperbolic groups, are given in the later sections.

Journal

Journal für die reine und angewandte Mathematik (Crelle's Journal) – de Gruyter

Published: Jun 1, 2008

References

  • simple On the dynamics and the fixed subgroup of a free group automorphism Invent
    Cohen