Precise asymptotics for periodic orbits of the geodesic flow in nonpositive curvature

Open Access
Gunesch, Roland
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
April 30, 2002
Committee Members:
  • John Metzner, Committee Member
  • Professor Dr Anatole B Katok, Committee Chair
  • Professor Dr Mark Levi, Committee Member
  • Professor Dr Serge Tabachnikov, Committee Member
  • dynamical systems
  • closed geodesics
  • Riemannian geometry
  • geodesic flows
  • measure of maximal entropy
  • nonpositive curvature
This thesis establishes the most precise asymptotic formula known for the number of homotopy classes of periodic orbits for the geodesic flow and proves it for any compact manifold of nonpositive curvature with geometric rank one. This extends a celebrated result of G.A. Margulis to the nonuniformly hyperbolic case and strengthens previous results by G. Knieper.