On the Existence of fixed points of the composition operator for circle maps
RESEAUX CEREBRAUX
PHYSIQUE STATISTIQUE
SYSTEMES COMPLEXES
THEORIES NON LINEAIRES
DYNAMIQUE
INFORMATIQUE QUANTIQUE
Abstract : In the theory of circle maps with golden ratio rotation number formulated by Feigenbaum, Kadanoff, and Shenker [FKS], and by Ostlund, Rand, Sethna, and Siggia [ORSS], a central role is played by fixed points of a certain composition operator in map space. We define a common setting for the problem of proving the existence of these fixed points and of those occurring in the theory of maps of the interval. We give a proof of the existence of the fixed points for a wide range of the parameters on which they depend.
EPSTEIN
ECKMANN
P/86/29
IHES
05/1986
A4
13 f.
EN
TEXTE
PREPUBLICATION
P_86_29.pdf
1986
Scaling of Mandelbrot sets generated by critical point preperiodicity
RESEAUX CEREBRAUX
PHYSIQUE STATISTIQUE
SYSTEMES COMPLEXES
THEORIES NON LINEAIRES
DYNAMIQUE
Astract : Letz?f?(z) be a complex holomorphic function depending holomorphically on the complex parameter ?. If, for ?=0, a critical point off0 falls after a finite number of steps onto an unstable fixed point off0, then, in the parameter space, near 0, an infinity of more and more accurate copies of the Mandelbrot set appears. We compute their scaling properties.
EPSTEIN
ECKMANN
P/83/70
IHES
11/1983
A4
8 f.
EN
TEXTE
PREPUBLICATION
P_83_70.pdf
1983
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
On the existence of Fegeinbaum's fixed point
RESEAUX CEREBRAUX
PHYSIQUE STATISTIQUE
ANALYSE FONCTIONNELLE
THEORIES NON LINEAIRES
DYNAMIQUE
Abstract : We give a proof of the existence of aC2, even solution of Feigenbaum's functional equation
g(x)=???10g(g(??0x)),g(0) = 1,
whereg is a map of [?1, 1] into itself. It extends to a real analytic function over ?.
EPSTEIN
CAMPANINO
P/80/35
IHES
1980
A4
38 f.
EN
TEXTE
PREPUBLICATION
P_80_35.pdf
1980
Time-ordered products and Schwinger functions
RESEAUX CEREBRAUX
THEORIE DES CHAMPS
SYSTEMES COMPLEXES
PHYSIQUE STATISTIQUE
Abstract : It is shown that every system of time-ordered products for a local field theory determines a related system of Schwinger functions possessing an extended form of Osterwalder-Schrader positivity and that the converse is true provided certain growth conditions are satisfied. This is applied to the ? 3 4 theory and it is shown that the time-ordered functions andS-matrix elements admit the standard perturbation series as asymptotic expansions.
EPSTEIN
ECKMANN
P/78/227
IHES
1978
A4
35 f.
EN
TEXTE
PREPUBLICATION
P_78_227.pdf
1978
Remarks on two theorems of E. Lieb
RESEAUX CEREBRAUX
PHYSIQUE STATISTIQUE
SYSTEMES COMPLEXES
DYNAMIQUE
THEORIES NON LINEAIRES
INFORMATIQUE QUANTIQUE
Abstract : The concavity of two functions of a positive matrixA, Tr exp(B + logA) and TrA r KA p K* (whereB=B* andK are fixed matrices), recently proved by Lieb, can also be obtained by using the theory of Herglotz functions.
EPSTEIN
P/73/41
IHES
02/1973
A4
9 f.
EN
TEXTE
PREPUBLICATION
P_73_41.pdf
1973
Renormalization of non polynomial Lagrangians in Jaffe's class
RESEAUX CEREBRAUX
PHYSIQUE STATISTIQUE
SYSTEMES COMPLEXES
DYNAMIQUE
THEORIES NON LINEAIRES
INFORMATIQUE QUANTIQUE
Abstract : t, It is shown how a renormalized perturbation series can be defined for a
theory with strictly locaI, non-polynomial, interacting Lagrangian
:A(x)r: 2e(x) = )__, t,-----
r=O r!
so as to preserve locality at every order.
EPSTEIN
GLASER
P/72/10
IHES
1972
A4
11 f.
EN
TEXTE
PREPUBLICATION
P_72_10.pdf
1972