## Dynamics of hyperbolic iwips

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- by Caglar Uyanik PDF
- Conform. Geom. Dyn.
**18**(2014), 192-216 Request permission

## 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 Martinâs original approach. The second proof uses the geometric intersection form of Kapovich and Lustig and relies on unique ergodicity results from symbolic dynamics.## References

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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
- Email: cuyanik2@illinois.edu
- 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 âRNMS: GEometric structures And Representation varietiesâ (the GEAR Network)
- © Copyright 2014 American Mathematical Society
- Journal: Conform. Geom. Dyn.
**18**(2014), 192-216 - MSC (2010): Primary 20F65
- DOI: https://doi.org/10.1090/S1088-4173-2014-00270-7
- MathSciNet review: 3273532