• On certain orbits of geodesic flow and $(a,b)$-continued fractions

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/131/0002

• # Keywords

Geodesic flow; modular surface; continued fractions; coding of geodesics.

• # 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.

• # Author Affiliations

1. Institute of Infrastructure Technology Research and Management, Near Khokhara Circle, Maninagar (East), Ahmedabad 380 026, India

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019