Editing Lyapunov exponent (section)

==Local Lyapunov exponent==

Whereas the (global) Lyapunov exponent gives a measure for the total predictability of a system, it is sometimes of interest to estimate the local predictability around a point {{math|''x''<sub>0</sub>}} in phase space. This may be done through the [[eigenvalues]] of the [[Jacobian matrix and determinant|Jacobian]] matrix {{math|''J''<sup>0</sup>(''x''<sub>0</sub>)}}.  These eigenvalues are also called local Lyapunov exponents.<ref>{{cite journal
|year=1992
|journal=Journal of Nonlinear Science
|volume=2
|issue=3
|doi=10.1007/BF01208929
|title=Local Lyapunov exponents computed from observed data
|last1=Abarbanel|first1=H.D.I.
|last2=Brown|first2=R.
|last3=Kennel|first3=M.B.|bibcode = 1992JNS.....2..343A|pages=343–365|s2cid=122542761
}}</ref> Local exponents are not invariant under a nonlinear change of coordinates.