On the discrete Godbillon-Vey invariant and Dehn surgery on geodesic flows
On the Entropy of the Geodesic Flow in Manifolds Without Conjugate Points.
On the Ergodicity of Frame Flows.
On the existence of escaping geodesics.
On the finite blocking property
A planar polygonal billiard is said to have the finite blocking property if for every pair of points in there exists a finite number of “blocking” points such that every billiard trajectory from to meets one of the ’s. Generalizing our construction of a counter-example to a theorem of Hiemer and Snurnikov, we show that the only regular polygons that have the finite blocking property are the square, the equilateral triangle and the hexagon. Then we extend this result to translation surfaces....
On the geodesics flow of tori without conjugate points.
On the Lengths of Closed Geodesics on Almost Round Spheres.
On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus
We find the minimum dilatation of pseudo-Anosov homeomorphisms that stabilize an orientable foliation on surfaces of genus three, four, or five, and provide a lower bound for genus six to eight. Our technique also simplifies Cho and Ham’s proof of the least dilatation of pseudo-Anosov homeomorphisms on a genus two surface. For genus to , the minimum dilatation is the smallest Salem number for polynomials of degree .
On the spectral theory and dynamics of asymptotically hyperbolic manifolds
We present a brief survey of the spectral theory and dynamics of infinite volume asymptotically hyperbolic manifolds. Beginning with their geometry and examples, we proceed to their spectral and scattering theories, dynamics, and the physical description of their quantum and classical mechanics. We conclude with a discussion of recent results, ideas, and conjectures.
Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature.
Packing dimensions, transversal mappings and geodesic flows.
Polynomial invariants for fibered 3-manifolds and teichmüller geodesics for foliations
Precise counting results for closed orbits of Anosov flows
Propriétés ergodiques du flot horocyclique d'une surface hyperbolique géométriquement finie
Propriétés ergodiques, en mesure infinie, de certains systèmes dynamiques fibrés
Prym Varieties and the Geodesic Flow on SO(n).
Quasiconformality in the Geodesic Flow of Negatively Curved Manifolds.
Quasilinear waves and trapping: Kerr-de Sitter space
In these notes, we will describe recent work on globally solving quasilinear wave equations in the presence of trapped rays, on Kerr-de Sitter space, and obtaining the asymptotic behavior of solutions. For the associated linear problem without trapping, one would consider a global, non-elliptic, Fredholm framework; in the presence of trapping the same framework is available for spaces of growing functions only. In order to solve the quasilinear problem we thus combine these frameworks with the normally...
Real analytic convex surfaces with positive topological entropy and rigid body dynamics.
Real and complex transversely symplectic Anosov flows of dimension five
Nous présentons plusieurs résultats de rigidité concernant les flots d’Anosov admettant transversalement des structures symplectiques réelles ou complexes de dimension .