New proofs of the existence of the Feigenbaum functions
Abstract
A new proof of the existence of analytic, unimodal solutions of the Cvitanović-Feigenbaum functional equation λ g( x) = - g( g(-λ x)), 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 [8] is recovered. The method also provides the existence of solutions for certain given values of r, and in particular, for r=2, a proof requiring no computer.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- September 1986
- DOI:
- 10.1007/BF01207254
- Bibcode:
- 1986CMaPh.106..395E