Analyticity properties of the Feigenbaum function
Abstract
Analyticity properties of the Feigenbaum function [a solution of g( x)=-λ-1 g( g(λ x)) with g(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 that g is analytic and uniform in a domain with a natural boundary.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- September 1981
- DOI:
- 10.1007/BF01209078
- Bibcode:
- 1981CMaPh..81..437E