Communications in Mathematical Physics

, Volume 81, Issue 3, pp 437–453

Analyticity properties of the Feigenbaum function

  • H. Epstein
  • J. Lascoux
Article

DOI: 10.1007/BF01209078

Cite this article as:
Epstein, H. & Lascoux, J. Commun.Math. Phys. (1981) 81: 437. doi:10.1007/BF01209078

Abstract

Analyticity properties of the Feigenbaum function [a solution ofg(x)=−λ−1g(gx)) withg(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 thatg is analytic and uniform in a domain with a natural boundary.

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • H. Epstein
    • 1
  • J. Lascoux
    • 2
  1. 1.Institut des Hautes Etudes ScientifiquesBures-sur-YvetteFrance
  2. 2.Centre de Physique Théorique, Ecole PolytechniquePalaiseauFrance