The objective of this note is to present some results, to be proved in a forthcoming paper,
about certain special solutions of the Euler-Lagrange equations on closed manifolds. Our …

Define the critical level c (L) of a convex superlinear Lagragian L as the infimum of the k∈
ℝsuch that the Lagragian L+ k has minimizers with fixed endpoints and free time interval. We …

Global Minimizers of Autonomous Lagrangians Page 1 Global Minimizers of Autonomous
Lagrangians Gonzalo Contreras Renato Iturriaga cimat mexico, gto. c 2000 Page 2 ii ii Page 3 …

The author considers dynamical systems generated by time-dependent periodic
Lagrangians on a closed manifold M. An invariant probability mu of such a system has an …

We prove that for a uniformly convex Lagrangian system L on a compact manifold M, almost
all energy levels contain a periodic orbit. We also prove that below Mañé's critical value of …

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 …

We study the action functional associated to a smooth Lagrangian function on the tangent
bundle of a manifold, having quadratic growth in the velocities. We show that, although the …

In this expository article we study the question of the existence of periodic orbits of
prescribed energy for classical Hamiltonian systems on compact configuration spaces. We …

In this paper we analyze and generalize, from the point of view of the maximum principle, a
class of nonlinear optimal control problems originally introduced in Brockett (1994). The …

It is proved here that minimizing measures of a Lagrangian flow are invariant and the
Lagrangian is cohomologous to a constant on the support of their ergodic components …