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Length Functions on Currents and Applications to Dynamics and Counting

In: In the Tradition of Thurston

Author

Listed:
  • Viveka Erlandsson

    (University of Bristol, School of Mathematics)

  • Caglar Uyanik

    (Yale University, Department of Mathematics)

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.

Suggested Citation

  • Viveka Erlandsson & Caglar Uyanik, 2020. "Length Functions on Currents and Applications to Dynamics and Counting," Springer Books, in: Ken’ichi Ohshika & Athanase Papadopoulos (ed.), In the Tradition of Thurston, chapter 0, pages 423-458, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-55928-1_11
    DOI: 10.1007/978-3-030-55928-1_11
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