Dynamics of hyperbolic iwips

Uyanik, Caglar

doi:10.1090/S1088-4173-2014-00270-7

Dynamics of hyperbolic iwips
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by Caglar Uyanik

Conform. Geom. Dyn. 18 (2014), 192-216

DOI: https://doi.org/10.1090/S1088-4173-2014-00270-7

Published electronically: October 23, 2014

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Abstract:

We present two proofs of the fact, originally due to Reiner Martin, that any fully irreducible hyperbolic element of $Out(F_N)$ acts on the projectivized space of geodesic currents $\mathbb {P}Curr(F_N)$ with uniform north-south dynamics. The first proof, using purely train-track methods, provides an elaborated and corrected version of Reiner Martin’s original approach. The second proof uses the geometric intersection form of Kapovich and Lustig and relies on unique ergodicity results from symbolic dynamics.

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