Length functions on currents and applications to dynamics and counting
Geometric Topology
2019-02-20 v2 Group Theory
Abstract
The aim of this (mostly expository) article is twofold. We first explore a variety of length functions on the space of currents, and we survey recent work regarding applications of length functions to counting problems. Secondly, we use length functions to provide a proof of a folklore theorem which states that pseudo-Anosov homeomorphisms of closed hyperbolic surfaces act on the space of projective geodesic currents with uniform north-south dynamics.
Cite
@article{arxiv.1803.10801,
title = {Length functions on currents and applications to dynamics and counting},
author = {Viveka Erlandsson and Caglar Uyanik},
journal= {arXiv preprint arXiv:1803.10801},
year = {2019}
}
Comments
35pp, 2 figures, comments welcome! Second version: minor corrections. To appear as a chapter in the forthcoming book "In the tradition of Thurston" edited by V. Alberge, K. Ohshika and A. Papadopoulos