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Dynamics of Free Group Automorphisms

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Combinatorial and Geometric Group Theory

Part of the book series: Trends in Mathematics ((TM))

Abstract

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

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Author information

Authors and Affiliations

  1. Department of Mathematics, The City College of CUNY, New York, NY, 10031, USA

    Peter Brinkmann

Authors
  1. Peter Brinkmann
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Editor information

Editors and Affiliations

  1. Mathematisches Institut der Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany

    Oleg Bogopolski

  2. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6, Canada

    Inna Bumagin

  3. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St., West, Montreal, Quebec, H3A 2K6, Canada

    Olga Kharlampovich

  4. Departament de Matematica Aplicada III, EPSEM — Universitat Politècnica de Catalunya, Av. Bases de Manresa 61-73, 08242, Manresa, Barcelona, Spain

    Enric Ventura

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Brinkmann, P. (2010). Dynamics of Free Group Automorphisms. In: Bogopolski, O., Bumagin, I., Kharlampovich, O., Ventura, E. (eds) Combinatorial and Geometric Group Theory. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9911-5_2

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