News proofs of the existence of the Feigenbaum functions

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/EPSTEIN/Depuis_1964/P_85_55/P_85_55.pdf

Epstein, Henri

EPSTEIN

10/1985

Abstract : A new proof of the existence of analytic, unimodal soutions of the Cvitanovic-Feigenbaum functional equation ?g (x) = -g(g-?x)), g(x) ? 1-const. |x| r at 0, walid for all ? in (0,1), is given, and the existence of the Eckmann-Wittwer functions [8] is recovered. The method also provides the existence of solutions for certain given values of r, and in particular, for r=2, a proof requiring no computer.

EQUATIONS FONCTIONNELLES

P/85/55

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EPSTEIN, “News proofs of the existence of the Feigenbaum functions,” Archives de l'IHES, consulté le 11 septembre 2024, https://omeka.ihes.fr/document/P_85_55.pdf.