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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 ?.
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…
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.
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…
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…