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- Collection: Epstein, Henri
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Existence and properties of p-tupling fixed points
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,…
Normal forms for parabolic partial differential equations
Abstract : We begin a study of normal form theorems for parabolic partial differential equations. We show that despite the presence of resonances one can construct a partial normal form for perturbations of the Ginzburg-Landau equation. The normal…
Fixed points of composition operators II
Abstract : Analytic unicritical fixed points of composition operators of Feigenbaum's type for inteval and circle maps are shown to exist for every value of r > 1, where r is the order of the critical point.
Fixed points of composition operators
Abstract : This extended version of lectures given at eht NATO advanced Study Institute on Non-Linear Evolution and Chaotic Phenomena held in June 1987 in Noto (Italy), and directed by G. Gallovotti, A. M. Anile and P. Zweifel, will appear in the…
Test of a probabilistic model of evolutionary success
Abstract : A proposed relation between spin glasses and biological evolution is given a precise form, using a probabilistic model called Generalized Random Energy Model (GREM). Here we test this idea using the taxonomic distribution of European…
On the Existence of fixed points of the composition operator for circle maps
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…
News proofs of the existence of the Feigenbaum functions
Abstract : A new proof of the existence of analytic, unimodal soutions of the Cvitanovic-Feigenbaum functional equation ?g (x) = -g(g-?x)), g(x) ? 1-const. |x| r at 0, walid for all ? in (0,1), is given, and the existence of the Eckmann-Wittwer…
Scaling of Mandelbrot sets generated by critical point preperiodicity
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…
Analyticity properties of the Feigenbaum function
Absract : Analyticity properties of the Feigenbaum function [a solution ofg(x)=???1g(g(?x)) withg(0)=1,g?(0)=0,g?(0)
On the existence of Fegeinbaum's fixed point
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 ?.
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 ?.
Borel summability of the mass and the s-matrix in ?4 models
Abstract : We show that in the ?{2/4} theory, the physical mass and the two-body S-matrix are Borel summable in the coupling constant ? at ?=0.
Time-ordered products and Schwinger functions
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…
Quelques Aspects globaux des problèmes d'Edge-of-the-wedge
Contribution au Colloque sur les Hyperfonctions et leurs applications, Nice, mai 1973
Abstract : Cet exposé décrit birèvement quelques résultats obtenus entre 1961et 1963. Certains d'entre eux ont été publiés dans [1], [2], [3]. D'autres…
Abstract : Cet exposé décrit birèvement quelques résultats obtenus entre 1961et 1963. Certains d'entre eux ont été publiés dans [1], [2], [3]. D'autres…
Remarks on two theorems of E. Lieb
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.
Renormalization of non polynomial Lagrangians in Jaffe's class
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.
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.
Non-positivity of the energy density in quantized field theories
Abstract : It is shown that a positive definite local energy density is incompatible with the usual postulates of local field theory. The question whether it can be bounded below is briefly discussed but not solved.