Abstract
For suitably defined largeN, we express Feigenbaum's equation as a singular Schroder functional equation whose solution is obtained using a scaling ansatz. In the limit of infiniteN certain self-consistency conditions on the scaled Schroder solution lead to an essentially singular solution of Feigenbaum's equation with a length scale factor of α≅ 0.0333 and. a limiting feigenvalue of δ∞≃30.50, in agreement with Eckmann and Wittwer's value of α=0.0333831... and their conjectured estimate of δ∞≲30.
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Thompson, C.J., McGuire, J.B. Asymptotic and essentially singular solutions of the Feigenbaum equation. J Stat Phys 51, 991–1007 (1988). https://doi.org/10.1007/BF01014896
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DOI: https://doi.org/10.1007/BF01014896