02 Feb
2021
On certain orbits of geodesic flow and (a, b)-continued fractions
Authors :- Manoj Choudhuri
Publication :- Proceedings - Mathematical Sciences, 131, Article number: 2 Feb.(2021)
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.