Quadratic irrationals and linking numbers of modular knots
Number Theory
2012-05-11 v1 Dynamical Systems
Abstract
A closed geodesic on the modular surface gives rise to a knot on the 3-sphere with a trefoil knot removed, and one can compute the linking number of such a knot with the trefoil knot. We show that, when ordered by their length, the set of closed geodesics having a prescribed linking number become equidistributed on average with respect to the Liouville measure. We show this by using the thermodynamic formalism to prove an equidistribution result for a corresponding set of quadratic irrationals on the unit interval.
Keywords
Cite
@article{arxiv.1205.2230,
title = {Quadratic irrationals and linking numbers of modular knots},
author = {Dubi Kelmer},
journal= {arXiv preprint arXiv:1205.2230},
year = {2012}
}