

A quantitative measure of the sensitive dependence on the initial conditions is
the Lyapunov exponent . It is the averaged rate of divergence (or convergence) of two neighboring
trajectories.
Actually there is a whole spectrum of Lyapunov exponents.
Their number is equal to the dimension of the phase space.
If one speaks about the Lyapunov exponent, the largest one is meant.
It is important because it determines the prediction horizon.
Even qualitative predictions are impossible for a time interval beyond this horizon.
It is given by
To obtain the Lyapunov spectra, imagine an infinitesimal small ball with radius dr sitting on the initial state of a trajectory. The flow will deform this ball into an ellipsoid. That is, after a finite time t all orbits which have started in that ball will be in the ellipsoid. The ith Lyapunov exponent is defined by 
QUESTIONS worth to think about: 
