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Bounds, quadratic differentials and renormalization conjectures
Abstract : In the context of smooth folding mappings we verifie certain conjecture by showing bounded return time renormalization is topologically hyperbolic and find the stable and unstable manifolds. The main consequence is the asymptotic geometric…
Renormalization group fixed points of general n-vector models
Abstract : We make a general study of symmetry and stability of the fixed points of the quartic Hamiltonian
of an n-component field (or order parameter} for n&4. Simple proofs of known results are given.
Among new results, we shou that when it…
of an n-component field (or order parameter} for n&4. Simple proofs of known results are given.
Among new results, we shou that when it…
The Symmetry and renormalization group fixed points of quadratic hamiltonians
Abstract : This paper studies the number and the nature of the fixed points of the renormalization group for the ?4 model, as used for instance in the Landau theory of second order phase transitions. It is shown that when it exists the stable fixed…
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,…
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…