A precise calculation of the Feigenbaum constants

Briggs, Keith

doi:10.1090/S0025-5718-1991-1079009-6

A precise calculation of the Feigenbaum constants
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Math. Comp. 57 (1991), 435-439 Request permission

Abstract:

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

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