Communications in Mathematical Physics

, Volume 79, Issue 2, pp 261–302

On the existence of Feigenbaum's fixed point

  • M. Campanino
  • H. Epstein
Article

DOI: 10.1007/BF01942063

Cite this article as:
Campanino, M. & Epstein, H. Commun.Math. Phys. (1981) 79: 261. doi:10.1007/BF01942063

Abstract

We give a proof of the existence of aC2, even solution of Feigenbaum's functional equation
$$g{\text{(}}x) = - \lambda _0^{ - 1} g{\text{(}}g( - \lambda _0 x)),g{\text{(0) = 1,}}$$
whereg is a map of [−1, 1] into itself. It extends to a real analytic function over ℝ.

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • M. Campanino
    • 1
  • H. Epstein
    • 1
  1. 1.Institut des Hautes Etudes ScientifiquesBures-sur-YvetteFrance
  2. 2.Istituto Matematico “G. Castelnuovo”Università degli studi di RomaRomaItaly