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
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
Lessons from quantum field theory, Hopf algebras and spacetime goemetries
THEORIE QUANTIQUE DES CHAMPS
GEOMETRIE NON COMMUTATIVE
RENORMALISATION
ALGEBRES DE HOPF
EQUATIONS DIFFERENTIELLES
CONNES
KREIMER
M/99/22
IHES
04/1999
A4
13 p.
EN
TEXTE
PREPUBLICATION
M_99_22.pdf
1999
On the Structure of infinitely many dynamical systems nested inside or outside a given one
SYSTEMES DYNAMIQUES
RENORMALISATION
PHYSIQUE
Abstract : In the content of smooth folding mappings we show 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 Teichmüller Contraction Principle to prove renormalization contraction in a space of holomorphic dynamical systems that contains the limit set of renormalization.
SULLIVAN
M/90/75
IHES
09/1990
A4
25 f.
EN
TEXTE
PREPUBLICATION
M_90_75.pdf
1990
On the Triviality ??d4 theories and the approach to the critical point in > (=) 4 dimensions
THEORIE DES CHAMPS
DIMENSIONS
RENORMALISATION
CHAMPS SCALAIRES
INEGALITES
CORRELATION
FROHLICH
P/81/41
IHES
1981
A4
14 f.
EN
TEXTE
PREPUBLICATION
P_81_41.pdf
1981
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
Renormalization in quantum field theory and the Riemann-Hilbert problem
THEORIE QUANTIQUE DES CHAMPS
RENORMALISATION
EQUATIONS DIFFERENTIELLES
CONNES
KREIMER
M/99/75
IHES
09/1999
A4
5 f.
EN
TEXTE
PREPUBLICATION
M_99_75.pdf
1999
Renormalization in quantum field theory and the Riemann-Hilbert problem I : the Hopf algebra structure of graphs and the main theorem
THEORIE QUANTIQUE DES CHAMPS
RENORMALISATION
EQUATIONS DIFFERENTIELLES
ALGEGRES DE HOPF
CONNES
KREIMER
M/99/91
IHES
12/1999
A4
19 f.
EN
TEXTE
PREPUBLICATION
M_99_91.pdf
1999
Renormalization in quantum field theory and the Riemann-Hilbert problem II : the ?-function, diffeomorphisms and the renormalization group
THEORIE QUANTIQUE DES CHAMPS
RENORMALISATION
EQUATIONS DIFFERENTIELLES
ALGEBRES DE HOPF
DIFFEOMORPHISMES
CONNES
KREIMER
M/00/22
IHES
03/2000
A4
19 f.
EN
TEXTE
PREPUBLICATION
M_00_22.pdf
2000
Scaling and functional integration. Suivi de Brydges' operator in renormalization theory
INTEGRATION DE FONCTIONS
RENORMALISATION
PHYSIQUE
ESPACE-TEMPS
EQUATIONS AUX DERIVEES PARTIELLES
ESPACES GENERALISES
CARTIER
DEWITT-MORETTE
M/99/51
IHES
07/1999
A4
12 f.
EN
TEXTE
PREPUBLICATION
M_99_51.pdf
1999
Symétries galoisiennes et renormalisation
RENORMALISATION
THEORIE DES CHAMPS
GROUPES DE SYMETRIE
THEORIE DES NOMBRES
CONNES
M/02/79
IHES
11/2002
A4
12 f.
FR
TEXTE
PREPUBLICATION
M_02_79.pdf
2002
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