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Digitale Medien

Asymptotic and essentially singular solutions of the Feigenbaum equation (1988)

Thompson, Colin J. ; McGuire, J. B.

Springer

Journal of statistical physics 51 (1988), S. 991-1007

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ISSN: 1572-9613

Schlagwort(e): Feigenbaum ; largeN ; iteration ; doubling transformation ; universal ; fixed point ; feigenvalue

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01014896

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