In mathematics, specifically bifurcation theory, the Feigenbaum constants /ˈfaɪɡənbaʊm/ δ and α are two mathematical constants which both express ratios in a bifurcation diagram for a non-linear map. They are named after the physicist Mitchell J. Feigenbaum.

Feigenbaum originally related the first constant to the period-doubling bifurcations in the logistic map, but also showed it to hold for all one-dimensional maps with a single quadratic maximum. As a consequence of this generality, every chaotic system that corresponds to this description will bifurcate at the same rate. Feigenbaum made this discovery in 1975, and he officially published it in 1978.

The first Feigenbaum constant or simply Feigenbaum constant δ 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 parameterized by the bifurcation parameter a.

It is given by the limit:

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

This gives its numerical value (sequence A006890 in the OEIS):

${\displaystyle \delta =4.669\,201\,609\,102\,990\,671\,853\,203\,820\,466\ldots }$