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Feigenbaum Function

Consider an arbitrary 1-D Map

\end{displaymath} (1)

at the onset of Chaos. After a suitable rescaling, the Feigenbaum function
g(x)=\lim_{n\to\infty} {1\over F^{(2^n)}(0)} F^{(2^n)}(xF^{(2^n)}(0))
\end{displaymath} (2)

is obtained. This function satisfies
g(g(x))=-{1\over\alpha} g(\alpha x),
\end{displaymath} (3)

with $\alpha=2.50290\ldots$, a quantity related to the Feigenbaum Constant.

See also Bifurcation, Chaos, Feigenbaum Constant


Grassberger, P. and Procaccia, I. ``Measuring the Strangeness of Strange Attractors.'' Physica D 9, 189-208, 1983.

© 1996-9 Eric W. Weisstein