On certain orbits of geodesic flow and (a,b)-continued fractions
arXiv:1703.09002
Abstract
In this article, we characterize two kinds of exceptional orbits of the geodesic flow associated with the Modular surface in terms of a two-parameter family of continued fraction expansion of endpoints of the lifts to the hyperbolic plane of the corresponding geodesics. As a consequence, we obtain an extension of Dani correspondence between homogeneous dynamics and Diophantine approximation.
Accepted for publication in " Proceedings - Mathematical Sciences, Indian Academy of Sciences "