# American Institute of Mathematical Sciences

January  2010, 26(1): 347-363. doi: 10.3934/dcds.2010.26.347

## Distortion and entropy for automorphisms of free groups

 1 University of Manchester, School of Mathematics, Oxford Road, Manchester M13 9PL, United Kingdom

Received  June 2008 Revised  August 2008 Published  October 2009

Recently, several numerical invariants have been introduced to characterize the distortion induced by automorphisms of a free group. We unify these by interpreting them in terms of an entropy function of a kind familiar in thermodynamic ergodic theory. We draw an analogy between this approach and the Manhattan curve associated to a pair of hyperbolic surfaces.
Citation: Richard Sharp. Distortion and entropy for automorphisms of free groups. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 347-363. doi: 10.3934/dcds.2010.26.347
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