BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gerhard Knieper (Ruhr University Bochum) DTSTART:20211124T121000Z DTEND:20211124T133000Z DTSTAMP:20260423T005742Z UID:GDS/42 DESCRIPTION:Title: Gro wth rate of closed geodesics on surfaces without conjugate points\nby Gerhard Knieper (Ruhr University Bochum) as part of Geometry and Dynamics seminar\n\n\nAbstract\nLet (M\,g) be a closed Riemannian surface of of gen us at least 2 and no \nconjugate points. By the uniformization theorem suc h a surface admits\na metric of negative curvature and therefore the topol ogical entropy h \nof the geodesic flow is positive. Denote by P(t) the n umber of free \nhomotopy classes containing a closed geodesic of period $ \\le t $. We \nwill show: P(t) is asymptotically equivalent to e^(ht)/(ht) =F(t)\, i.e. \nthe ratio of P and F converges to 1 as t tends to infinit y. \nAn important ingredient in the proof is a mixing flow invariant measu re \ngiven by the unique measure of maximal entropy. Under suitable hyperb olicity \nassumptions this result carries over to closed Riemannian manifo lds without \nconjugate and higher dimension.\n\nFor closed manifolds of n egative curvature the above estimate is well known \nand has been original ly obtained by Margulis. In a recent preprint\nthe estimate has been also obtained by Ricks for certain closed manifolds \n(rank 1 mflds) of non-po sitive curvature. This is a joint work with Vaughn \nClimenhaga and Khadim War.\n LOCATION:https://researchseminars.org/talk/GDS/42/ END:VEVENT END:VCALENDAR