Closed Legendre geodesics in Sasaki manifolds.
Connecting orbits of time dependent Lagrangian systems
We generalize to higher dimension results of Birkhoff and Mather on the existence of orbits wandering in regions of instability of twist maps. This generalization is strongly inspired by the one proposed by Mather. However, its advantage is that it contains most of the results of Birkhoff and Mather on twist maps.
Counting rational curves of arbitrary shape in projective spaces.