  From a kinematical point of view, the geometrical information of hamiltonian
chaos is given by the (un)stable directions, while the dynamical information is
given by the Lyapunov exponents. The finite time Lyapunov exponents are of
particular importance in physics. The spatial variations of the finite time
Lyapunov exponent and its associated (un)stable direction are related. Both of
them are found to be determined by a new hamiltonian of same number of degrees
of freedom as the original one. This new hamiltonian defines a flow field with
characteristically chaotic trajectories. The direction and the magnitude of the
phase flow field give the (un)stable direction and the finite time Lyapunov
exponent of the original hamiltonian. Our analysis was based on a $1{1\over 2}$
degree of freedom hamiltonian system.
