Abstract
We use the relation between the volumes of the strata of mero- morphic quadratic differentials with at most simple poles on CP 1 and counting functions of the number of (bands of) closed geodesics in associated flat met- rics with singularities to prove a very explicit formula for the volume of each such stratum conjectured by M. Kontsevich a decade ago. Applying ergodic techniques to the Teichmuller geodesic flow we obtain quadratic asymptotics for the number of (bands of) closed trajectories and for the number of generalized diagonals in almost all right-angled billiards.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Annales scientifiques de l'École normale supérieure
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.