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Distribution of intersection lengths of a random geodesic with a geodesic lamination

Published online by Cambridge University Press:  03 May 2007

MARTIN BRIDGEMAN  and
DAVID DUMAS
MARTIN BRIDGEMAN
Affiliation:
Department of Mathematics, Boston College, Chestnut Hill, MA 02467, USA (e-mail: [email protected])
DAVID DUMAS
Affiliation:
Department of Mathematics, Brown University, Providence, RI 02912, USA (e-mail: [email protected])
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Abstract

We investigate the distribution of lengths obtained by intersecting a random geodesic with a geodesic lamination. We give an explicit formula for the distribution for the case of a maximal lamination and show that the distribution is independent of the surface and lamination. We also show how the moments of the distribution are related to the Riemann zeta function.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 4 , August 2007 , pp. 1055 - 1072
Copyright
2007 Cambridge University Press

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