Local Lyapunov Exponent
Whereas the (global) Lyapunov exponent gives a measure for the total predictability of a system, it is sometimes interesting to estimate the local predictability around a point x0 in phase space. This may be done through the eigenvalues of the Jacobian matrix J 0(x0). These eigenvalues are also called local Lyapunov exponents. (A word of caution: unlike the global exponents, these local exponents are not invariant under a nonlinear change of coordinates.)
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