  The {\it curvature} and the {\it reduced curvature} are basic differential
invariants of the pair: (Hamiltonian system, Lagrange distribution) on the
symplectic manifold. We show that negativity of the curvature implies that any
bounded semi-trajectory of the Hamiltonian system tends to a hyperbolic
equilibrium, while negativity of the reduced curvature implies the
hyperbolicity of any compact invariant set of the Hamiltonian flow restricted
to a prescribed energy level. Last statement generalizes a well-known property
of the geodesic flows of Riemannian manifolds with negative sectional
curvatures.
