North-South dynamics of hyperbolic free group automorphisms on the space of currents
Abstract
Let $\varphi$ be a hyperbolic outer automorphism of a non-abelian free group $F_N$ such that $\varphi$ and $\varphi^{-1}$ admit absolute train track representatives. We prove that $\varphi$ acts on the space of projectivized geodesic currents on $F_N$ with generalized uniform North-South dynamics.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2015
- DOI:
- 10.48550/arXiv.1509.05443
- arXiv:
- arXiv:1509.05443
- Bibcode:
- 2015arXiv150905443L
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Dynamical Systems;
- Mathematics - Geometric Topology;
- 20F65
- E-Print:
- v3, 35pp, 2 figures. Major revisions following reviewer's comments