Bounds, quadratic differentials and renormalization conjectures
RENORMALISATION
PHYSIQUE
THEOREME DU POINT FIXE
ANALYSE VECTORIELLE
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 rigidity of the Cantor sets defined by the critical orbits. We use the bounds and quadratic differentials on Riemann surface lamination to prove exponential renormalization contraction in a space of holomorphic dynamical systems that contains the limit set of renormalization.
SULLIVAN
M/91/25
IHES
03/1991
A4
25 f.
EN
TEXTE
PREPUBLICATION
M_91_25.pdf
1991
Renormalization group fixed points of general n-vector models
RENORMALISATION
PHYSIQUE
THEOREME DU POINT FIXE
ANALYSE VECTORIELLE
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 exists the stable fixed point is unique; we give some precision
on its symmetry and on its attractor basin.
MICHEL
P/83/35
IHES
06/1983
A4
14 f.
EN
TEXTE
PREPUBLICATION
P_83_35.pdf
1983
The Symmetry and renormalization group fixed points of quadratic hamiltonians
THEOREME DU POINT FIXE
RENORMALISATION
GROUPES DE SYMETRIE
OPERATEUR HAMILTONIEN
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 point is unique and a condition on its symmetry is given: it is often larger than the initial symmetry.
Finally counter examples, with v arbitrarily large, are given to the Dzyaloshinskii conjecture that there exist no stable fixed points when the Landau potential depends on more than V = 3 parameters.
MICHEL
P/82/10
IHES
03/1982
A4
15 f.
EN
TEXTE
PREPUBLICATION
P_82_10.pdf
1982
A Shorter proof of the existence of the Feigenbaum fixed point
TOPOLOGIE
OPERATEURS NON LINAIRES
DEMONSTRATION
THEOREME DU POINT FIXE
LANFORD
M/84/39
IHES
08/1984
A4
11 f.
EN
TEXTE
PREPUBLICATION
M_84_39.pdf
1984
Existence and properties of p-tupling fixed points
RENORMALISATION
CARTOGRAPHIE
THEOREME DU POINT FIXE
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, univalence, behavior as r tends to infinity.
EPSTEIN
P/00/25
IHES
03/2000
A4
19 f.
EN
TEXTE
PREPUBLICATION
P_00_25.pdf
2000
Fixed points of composition operators II
TOPOLOGIE
THEOREME DU POINT FIXE
OPERATEURS DE COMPOSITION
THEORIE DES POINTS CRITIQUES
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.
EPSTEIN
P/88/21
IHES
04/1988
A4
5 f.
EN
TEXTE
PREPUBLICATION
P_88_21.pdf
1988
Fixed points of composition operators
TOPOLOGIE
THEOREME DU POINT FIXE
OPERATEURS DE COMPOSITION
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 proceedings of that institute. It gives a review of the proofs of the existence of fixed points of composition operators (of Feigenbaum's type) for interval and circle maps obtained by J.-P. Eckmann and the author [E], [EE]. In addition, the fixed-r method is shown to word for all r > 1 in the case of the interval (r characterizez the order of the critical point of solutions) ; the solutions are shown to have inverses univalent in the upper and lower half-planes, and, in the case of the interval, for even integer r, to be polynomial-like in the sense of Douady and Hubbard [DH].
EPSTEIN
P/87/36
IHES
09-1987
A4
17 f.
EN
TEXTE
PREPUBLICATION
P_87_36.pdf
1987