Feigenbaum Constants - The First Constant

The First Constant

The first Feigenbaum constant is the limiting ratio of each bifurcation interval to the next between every period doubling, of a one-parameter map

where f(x) is a function parametrized by the bifurcation parameter a.

It is given by the limit:

where an are discrete values of a at the nth period doubling.

According to (sequence A006890 in OEIS), this number to 30 decimal places is: δ = 4.669 201 609 102 990 671 853 203 821 578(...).

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