A Precise Calculation of the Feigenbaum Constants

Abstract

The Feigenbaum constants arise in the theory of iteration of real functions. We calculate here to high precision the constants a and S associated with period-doubling bifurcations for maps with a single maximum of order z , for 2 < z < 12. Multiple-precision floating-point techniques are used to find a solution of Feigenbaum's functional equation, and hence the constants.