Communications in Mathematical Physics

, Volume 106, Issue 3, pp 395–426

New proofs of the existence of the Feigenbaum functions

  • H. Epstein

DOI: 10.1007/BF01207254

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 [8] 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.

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • H. Epstein
    • 1
  1. 1.Institut des Hautes Etudes ScientifiquesBures-sur-YvetteFrance

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