Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Distortion and entropy for automorphisms of free groups

Pages: 347 - 363, Volume 26, Issue 1, January 2010      doi:10.3934/dcds.2010.26.347

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Richard Sharp - University of Manchester, School of Mathematics, Oxford Road, Manchester M13 9PL, United Kingdom (email)

Abstract: 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.

Keywords:  Free groups, automorphisms, distortion spectrum, subshifts of finite typ, thermodynamic formalism, entropy.
Mathematics Subject Classification:  Primary: 20F65, 20F67, 20F69, 37C35, 37D35; Secondary: 20E05, 37C30.

Received: June 2008;      Revised: August 2008;      Available Online: October 2009.