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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
)/
max,
is the error
of the measurment of the initial state.
Here, the error is given in units of the averaged amplitude of the nonperiodic oscillation.
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QUESTIONS worth to think about: |
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