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Conformal Geometry and Dynamics

ISSN 1088-4173



Dynamics of hyperbolic iwips

Author: Caglar Uyanik
Journal: Conform. Geom. Dyn. 18 (2014), 192-216
MSC (2010): Primary 20F65
Published electronically: October 23, 2014
MathSciNet review: 3273532
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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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Additional Information

Caglar Uyanik
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801

Received by editor(s): March 16, 2014
Received by editor(s) in revised form: May 24, 2014, and July 28, 2014
Published electronically: October 23, 2014
Additional Notes: The author was partially supported by the NSF grants of Ilya Kapovich (DMS-0904200) and Christopher J. Leininger (DMS-1207183) and also acknowledges support from U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 “RNMS: GEometric structures And Representation varieties” (the GEAR Network)
Article copyright: © Copyright 2014 American Mathematical Society