- 97-471 G. Contreras, R. Iturriaga
- Convex Hamiltonians without Conjugate Points.
Sep 2, 97
(auto. generated ps),
of related papers
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.