Abstract
Analyticity properties of the Feigenbaum function [a solution ofg(x)=−λ−1 g(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.
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Communicated by D. Ruelle
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Epstein, H., Lascoux, J. Analyticity properties of the Feigenbaum function. Commun.Math. Phys. 81, 437–453 (1981). https://doi.org/10.1007/BF01209078
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DOI: https://doi.org/10.1007/BF01209078