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

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      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

       

      MANOJ CHOUDHURI1

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

       
  • Proceedings – Mathematical Sciences | News

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