Oscar Erasmus Lanford III (January 6, 1940 – November 16, 2013) was an American mathematician working on mathematical physics and dynamical systems theory.

Lanford gave the first proof that the Feigenbaum-Cvitanovic functional equation has an even analytic solution g and that this fixed point g of the Feigenbaum renormalisation operator T is hyperbolic with a one-dimensional unstable manifold.

Feigenbaum has studied the logistic family and looked at the sequence of Period doubling bifurcations.

which is a "universal number" independent of the map f. The bifurcation diagram has become an icon of chaos theory.

Campanino and Epstein also gave a proof of the fixed point without computer assistance but did not establish its hyperbolicity.

The hyperbolicity is essential to verify the picture discovered numerically by Feigenbaum and independently by Coullet and Tresser.

Work of Sullivan later showed that the fixed point is unique in the class of real valued quadratic like germs.

Lanford was the recipient of the 1986 United States National Academy of Sciences award in Applied Mathematics and Numerical Analysis and holds an honorary doctorate from Wesleyan University.