Length Functions on Currents and Applications to Dynamics and Counting

Viveka Erlandsson () and Caglar Uyanik ()
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Viveka Erlandsson: University of Bristol, School of Mathematics
Caglar Uyanik: Yale University, Department of Mathematics

Chapter Chapter 11 in In the Tradition of Thurston, 2020, pp 423-458 from Springer

Abstract: Abstract The aim of this chapter 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.

Keywords: Teichmüller spaces; Geodesic laminations; Currents; Mapping class group; 37E30 (primary); 30F60, 57M50 (secondary) (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-55928-1_11

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DOI: 10.1007/978-3-030-55928-1_11

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