Category:First Feigenbaum Constant
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This category contains results about First Feigenbaum Constant.
Definitions specific to this category can be found in Definitions/First Feigenbaum Constant.
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.
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