Analyticity properties of the Feigenbaum function
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- Epstein, H. & Lascoux, J. Commun.Math. Phys. (1981) 81: 437. doi:10.1007/BF01209078
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Analyticity properties of the Feigenbaum function [a solution ofg(x)=−λ−1g(g(λx)) 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.