Géométrie sous-riemannienne
Geometry of the rolling ellipsoid
We study rolling maps of the Euclidean ellipsoid, rolling upon its affine tangent space at a point. Driven by the geometry of rolling maps, we find a simple formula for the angular velocity of the rolling ellipsoid along any piecewise smooth curve in terms of the Gauss map. This result is then generalised to rolling any smooth hyper-surface. On the way, we derive a formula for the Gaussian curvature of an ellipsoid which has an elementary proof and has been previously known only for dimension two....
Harmonic maps in three dimensional Minkowski space with image near geodesics.
Hofer's L...-geometry: energy and stability of Hamiltonian flows, part I.
Hofer's L...-geometry: energy and stability of Hamiltonian flows, part II.
Hofer's L...-geometry: energy and stability of Hamiltonian flows, part II (Erratum).
Hybrid robust stabilization in the Martinet case
Invariant distances and invariant differential metrics in locally convex spaces
Involution-invariant geodesics.
Light rays in static spacetimes with critical asymptotic behavior: a variational approach.
Manifolds with Geodesic Chords of Constant Length.
Metrics with only finitely many isometry invariant geodesics.
Morse index and bifurcation of p-geodesics on semi Riemannian manifolds
Given a one-parameter family of semi Riemannian metrics on an n-dimensional manifold M, a family of time-dependent potentials and a family of trajectories connecting two points of the mechanical system defined by , we show that there are trajectories bifurcating from the trivial branch if the generalized Morse indices and are different. If the data are analytic we obtain estimates for the number of bifurcation points on the branch and, in particular, for the number of strictly conjugate...
Morse-Sard theorem for closed geodesics
Multiple closed orbits for singular conservative systems via geodesic theory
Multiplicity and stability of closed geodesics on Finsler 2-spheres
A survey of recent progress on the multiplicity and stability problems for closed geodesics on Finsler 2-spheres is given.
Non-hyperbolic closed geodesics.
On the Equivariant Morse Chain Complex of the Space of Closed Curves.
On the Existence of Closed Geodesics on Spherical Manifolds.
On the existence of escaping geodesics.