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arXiv · 1205.2230

Quadratic irrationals and linking numbers of modular knots

Dubi Kelmer
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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.

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Dubi Kelmer. 2012-05-10. Quadratic irrationals and linking numbers of modular knots. https://arxiv.org/abs/1205.2230

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