Category:Definitions/First Feigenbaum Constant

This category contains definitions related to First Feigenbaum Constant.
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The first Feigenbaum constant is the limiting ratio of each bifurcation interval to the next between every period doubling of a one-parameter mapping:

$x_{i + 1} = \map f {x_i}$

where $\map f x$ is a function parameterized by the bifurcation parameter $a$.

It is given by the limit:

$\ds \delta = \lim_{n \mathop \to \infty} \dfrac{a_ {n - 1} - a_{n - 2} } {a_n - a_{n - 1} } = 4 \cdotp 66920 \, 16091 \, 02990 \, 67185 \, 32038 \, 20466 \, 20161 \, 72 \ldots$

where $a_n$ are discrete values of $a$ at the $n$th period doubling.