Length functions on currents and applications to dynamics and counting

Viveka Erlandsson; Caglar Uyanik

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arXiv · 1803.10801

Length functions on currents and applications to dynamics and counting

Viveka Erlandsson·Caglar Uyanik

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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.

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Viveka Erlandsson, Caglar Uyanik. 2018-03-28. Length functions on currents and applications to dynamics and counting. https://arxiv.org/abs/1803.10801

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