  We show that Gutzwiller's characterization of chaotic Hamiltonian systems in
terms of the curvature associated with a Riemannian metric tensor in the
structure of the Hamiltonian can be extended to a wide class of potential
models of standard form through definition of a conformal metric. The geodesic
equations reproduce the Hamilton equations of the original potential model when
a transition is made to the dual manifold, and the geodesics in the dual space
coincide with the orbits of the Hamiltonian potential model. We therefore find
a direct geometrical description of the time development of a Hamiltonian
potential model. The second covariant derivative of the geodesic deviation in
this dual manifold generates a dynamical curvature, resulting in (energy
dependent) criteria for unstable behavior different from the usual Lyapunov
criteria. We discuss some examples of unstable Hamiltonian systems in two
dimensions giving, in particular, detailed results for a potential obtained
from a fifth order expansion of a Toda lattice Hamiltonian.
