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Mathematics of Computation

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A precise calculation of the Feigenbaum constants

Author: Keith Briggs
Journal: Math. Comp. 57 (1991), 435-439
MSC: Primary 11Y60; Secondary 39B12, 58F14, 65Q05
MathSciNet review: 1079009
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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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Article copyright: © Copyright 1991 American Mathematical Society

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