On the Nature of turbulence
RESEAUX
PHYSIQUE STATISTIQUE
SYSTEMES COMPLEXES
SYSTEMES DYNAMIQUES
INFORMATIQUE QUANTIQUE
SYSTEMES NON LINEAIRES
Abstract : A mechanism for the genetration of turbulence and related phenomena in dissipative systems is proposed.
RUELLE
TAKENS
P/70/X036
IHES
05/1970
A4
16 f.
EN
TEXTE
PREPUBLICATION
P_70_X036.pdf
1970
Observables at Infinity and States with Short Range : Correlations in Statistical Mechanics
MECANIQUE STATISTIQUE
FONCTIONS DE CORRELATION
INFORMATIQUE QUANTIQUE
THEORIE DES TREILLIS
Abstract : We say that a representation of an algebra of local observables has short-range correlations if any observable which can be measured outside all bounded sets is a multiple of the identity, and that a state has finite range correlations if the corresponding cyclic representation does. We characterize states with short-range correlations by a cluster property. For classical lattice systems and continuous systems with hard cores, we give a definition of equilibrium state for a specific interaction, based on a local version of the grand canonical prescription; an equilibrium state need not be translation invariant. We show that every equilibrium state has a unique decomposition into equilibrium states with short-range correlations. We use the properties of equilibrium states to prove some negative results about the existence of metastable states. We show that the correlation functions for an equilibrium state satisfy the Kirkwood-Salsburg equations; thus, at low activity, there is only one equilibrium state for a given interaction, temperature, and chemical potential. Finally, we argue heuristically that equilibrium states are invariant under time-evolution.
LANDFORD
RUELLE
P/69/12
IHES
[06/1969]
A4
42 f.
EN
TEXTE
PREPUBLICATION
P_69_12.pdf
1969
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
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
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