English

Dynamics of hyperbolic iwips

Group Theory 2019-07-17 v4 Dynamical Systems Geometric Topology

Abstract

We present two proofs of the fact, originally due to Reiner Martin, that any fully irreducible hyperbolic element of Out(FN)Out(F_N) acts on the projectivized space of geodesic currents PCurr(FN)\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.

Keywords

Cite

@article{arxiv.1401.1557,
  title  = {Dynamics of hyperbolic iwips},
  author = {Caglar Uyanik},
  journal= {arXiv preprint arXiv:1401.1557},
  year   = {2019}
}

Comments

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

R2 v1 2026-06-22T02:40:56.800Z