Existence and properties of p-tupling fixed points
RENORMALISATION
CARTOGRAPHIE
THEOREME DU POINT FIXE
Abstract : We prove the existence of fixed points of p-tupling renormalization operators for interval and circle mappings having a critical point of arbitrary real degree r > 1. Some properties of the resulting maps are studied: analyticity, univalence, behavior as r tends to infinity.
EPSTEIN
P/00/25
IHES
03/2000
A4
19 f.
EN
TEXTE
PREPUBLICATION
P_00_25.pdf
2000
Analyticity properties of the Feigenbaum function
RESEAUX CEREBRAUX
PHYSIQUE STATISTIQUE
SYSTEMES COMPLEXES
THEORIES NON LINEAIRES
DYNAMIQUE
INFORMATIQUE QUANTIQUE
Absract : Analyticity properties of the Feigenbaum function [a solution ofg(x)=???1g(g(?x)) 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.
EPSTEIN
LASCOUX
P/81/27
IHES
05/1981
A4
27 f.
EN
TEXTE
PREPUBLICATION
P_81_27.pdf
1981