New proofs of the existence of the Feigenbaum functions
- Cite this article as:
- Epstein, H. Commun.Math. Phys. (1986) 106: 395. doi:10.1007/BF01207254
A new proof of the existence of analytic, unimodal solutions of the Cvitanović-Feigenbaum functional equation λg(x) = −g(g(−λx)),g(x) ≈ 1 - const|x|r at 0, valid for all λ in (0, 1), is given, and the existence of the Eckmann-Wittwer functions  is recovered. The method also provides the existence of solutions for certain given values ofr, and in particular, forr=2, a proof requiring no computer.