Distribution of approximants and geodesic flows
Abstract
We give a new proof of Moeckel's result that for any finite index subgroup of the modular group, almost every real number has its regular continued fraction approximants equidistributed into the cusps of the subgroup according to the weighted cusp widths. Our proof uses a skew product over a crosssection for the geodesic flow on the modular surface. Our techniques show that the same result holds true for approximants found by Nakada's \alphacontinued fractions, and also that the analogous result holds for approximants that are algebraic numbers given by any of Rosen's \lambdacontinued fractions, related to the infinite family of Hecke triangle Fuchsian groups.
 Publication:

arXiv eprints
 Pub Date:
 August 2012
 arXiv:
 arXiv:1208.0131
 Bibcode:
 2012arXiv1208.0131F
 Keywords:

 Mathematics  Dynamical Systems;
 37E05;
 11K50;
 30B70
 EPrint:
 16 pages