, Volume 81, Issue 3, pp 437-453

Analyticity properties of the Feigenbaum function

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Abstract

Analyticity properties of the Feigenbaum function [a solution ofg(x)=−λ−1 g(gx)) withg(0)=1,g′(0)=0,g″(0)<0] are investigated by studying its inverse function which turns out to be Herglotz or anti-Herglotz on all its sheets. It is found thatg is analytic and uniform in a domain with a natural boundary.

Communicated by D. Ruelle