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Last updated: Mon Nov 17 2008

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Schwarzian Derivative

The Schwarzian derivative is defined by

D_(Schwarzian)=(f^(''')(x))/(f^'(x))-3/2[(f^('')(x))/(f^'(x))]^2.

The Feigenbaum constant is universal for one-dimensional maps if its Schwarzian derivative is negative in the bounded interval (Tabor 1989, p. 220).

SEE ALSO: Feigenbaum Constant

REFERENCES:

Tabor, M. Chaos and Integrability in Nonlinear Dynamics: An Introduction. New York: Wiley, 1989.




CITE THIS AS:

Weisstein, Eric W. "Schwarzian Derivative." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SchwarzianDerivative.html

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