Ratios..........his 1st..........
The first constant[edit]
The first Feigenbaum constant is the limiting
ratio of each bifurcation interval to the next between every
period doubling, of a one-
parameter map
![{\displaystyle x_{i+1}=f(x_{i}),}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f54ed70444fa95742380f2ff40fc40bbd70bbd0)
where
f(x) is a function parameterized by the
bifurcation parameter a.
It is given by the
limit[2]
![{\displaystyle \delta =\lim _{n\to \infty }{\frac {a_{n-1}-a_{n-2}}{a_{n}-a_{n-1}}}=4.669\,201\,609\,\ldots ,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2dce01d320459df0cb12f281c1ca398651718fdd)
where
an are discrete values of
a at the
n-th period doubling.
According to (sequence
A006890 in the
OEIS), this number to 30 decimal places is
δ =
4.669201609102990671853203821578….
Illustration[edit]
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