We study deformations of compact Riemannian manifolds of negative curvature. We give an equation for the infinitesimal conjugacy between geodesic flows. This in turn allows us to compute derivatives of intersection of metrics. As a consequence we obtain a proof of a theorem of Wolpert.
We show that Lissajous knots are equivalent to billiard knots in a cube. We consider also knots in general 3-dimensional billiard tables. We analyse symmetry of knots in billiard tables and show in particular that the Alexander polynomial of a Lissajous knot is a square modulo 2.
We consider a class of flows which includes both magnetic flows and Gaussian thermostats of external fields. We give sufficient conditions for such flows on manifolds of negative sectional curvature to be Anosov.
Recently Entov and Polterovich asked if the Grubb measure was the only symplectic topological measure on the torus. Much to our surprise we discovered a whole new class of intrinsic simple topological measures on the torus, many of which were symplectic.
We extend here results for escapes in any given direction of the configuration space of a mechanical system with a non singular bounded at infinity homogeneus potential of degree -1, when the energy is positive. We use geometrical methods for analyzing the parallel and asymptotic escapes of this type of systems. By using Riemannian geometry methods we prove under suitable conditions on the potential that all the orbits escaping in a given direction are asymptotically parallel among themselves. We...
There is a class of metrics on the tangent bundle of a Riemannian manifold (oriented , or non-oriented, respectively), which are ’naturally constructed’ from the base metric [Kow-Sek1]. We call them “-natural metrics" on . To our knowledge, the geometric properties of these general metrics have not been studied yet. In this paper, generalizing a process of Musso-Tricerri (cf. [Mus-Tri]) of finding Riemannian metrics on from some quadratic forms on to find metrics (not necessary Riemannian)...