Computing a Solution of Feigenbaum's Functional Equation in Polynomial Time

TL;DR

This paper proves that the analytic solution to Feigenbaum's functional equation can be computed in polynomial time, making the Feigenbaum constant a polynomial time computable real number.

Contribution

It demonstrates that the solution to Feigenbaum's equation is polynomial time computable, advancing understanding of its computational complexity.

Findings

Feigenbaum's solution is polynomial time computable

The first Feigenbaum constant is a polynomial time computable real number

Establishes a link between analytic solutions and computational complexity

Abstract

Lanford has shown that Feigenbaum's functional equation has an analytic solution. We show that this solution is a polynomial time computable function. This implies in particular that the so-called first Feigenbaum constant is a polynomial time computable real number.