The Algebraic Integrability of Geodesic Flow on S0(4).
The Circle Problem on Surfaces of Variable Negative Curvature.
The Convergence of Zeta Functions for Certain Geodesic Flow Depends on Their Pressure.
The Intersection of Four Quadrics in IP6, Abelian Surfaces and their Moduli.
The magnetic geodesic flow on a homogeneous symplectic manifold.
The return sequence of the Bowen-Series map for punctured surfaces
For a non-compact hyperbolic surface M of finite area, we study a certain Poincaré section for the geodesic flow. The canonical, non-invertible factor of the first return map to this section is shown to be pointwise dual ergodic with return sequence (aₙ) given by aₙ = π/(4(Area(M) + 2π)) · n/(log n). We use this result to deduce that the section map itself is rationally ergodic, and that the geodesic flow associated to M is ergodic with respect to the Liouville measure. ...
The Teichmüller geodesic flow and the geometry of the Hodge bundle
The Teichmüller geodesic flow is the flow obtained by quasiconformal deformation of Riemann surface structures. The goal of this lecture is to show the strong connection between the geometry of the Hodge bundle (a vector bundle over the moduli space of Riemann surfaces) and the dynamics of the Teichmüller geodesic flow. In particular, we shall provide geometric criterions (based on the variational formulas derived by G. Forni) to detect some special orbits (“totally degenerate”) of the Teichmüller...
Topological properties of a rotation function in the integrable Jacobi problem for geodesics on ellipsoids
Torsion and closed geodesics on complex hyperbolic manfolds.
Two remarks about the connection of Jacobi and Neumann integrable systems.