G. Contreras, R. Iturriaga
Convex Hamiltonians without Conjugate Points.
(198K, LaTeX)

ABSTRACT.  We construct the Green bundles for an energy level without conjugate
points of a convex Hamiltonian. In this case we give a formula for 
the metric entropy of the Liouville measure and prove that the 
exponencial map is a local diffeomorphism. We also prove that the
Hamiltonian flow is Anosov if and only if the Green bundles are
transversal. Using the Clebsch transformation of the index form 
we prove that if the unique minimizing measure of a generic Lagrangian 
is supported on a periodic orbit, then it is a hyperbolic periodic orbit.
We also show some examples of differences with the behaviour of a 
geodesic flow without conjugate points, namely: 
(non-contact) flows and periodic orbits without invariant 
transversal bundles, segments without conjugate points but with
crossing solutions and non-surjective exponencial maps.