Dynamics of hyperbolic iwips

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.

v4: Revised following the referee's comments, includes the former appendix from arXiv:1311.1470 and a new proof of north-south dynamics

References in corpus (1)

• Generalized north-south dynamics on the space of geodesic currents

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