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
Physical implications of crystal symmetry and time reversal
RESEAUX CRISTALLINS
SYMETRIE
ESPACE ET TEMPS
Lectures given at the international school on Symmetry and Structural Properties of Condensed Matter. August 28 - September 5, 1996, Zajaczkowo (Posnan), Poland.
MICHEL
P/96/80
IHES
12/1996
A4
13 f.
EN
TEXTE
PREPUBLICATION
P_96_80.pdf
1996
Extrema of P-invariant functions on the Brillouin zone
ZONES DE BRILLOUIN
THEORIE DE MORSE
MAXIMUMS ET MINIMUMS
CRISTALLOGRAPHIE
MATHEMATIQUES
SYMETRIE
PHYSIQUE
Exapnded version of a lecture fiven at Naples, on October 25, 1991 at a Colloquium in memory of Léon Vanhove
Abstract : This paper studies the number of extrema (and their positions) of a countinuous Morse function on the Brillouin zone, when it is invariant by the point group symmetry of the crystal. Forty years ago, Vanhove had shown the importance of this problem in physics, but he could use only the crystal translational symmetry. In that case Morse theory predicts at least eight extrema. With the added use of general symmetry arguments we show that this number is larger for six of the 14 classes of Bravais lattices ; moreover it is possible to give the position of the extrema (and their nature) for 30 of the 73 arithmetic classes.This paper is written for a larger audience than that of solid state physicists ; it also defines carefully the necessary crystallographic concepts which are generally poorly understood in the solid state literature.
MICHEL
P/92/16
IHES
04/1992
A4
13 f.
EN
TEXTE
PREPUBLICATION
P_92_16.pdf
1992
Compte-rendu du comité scientifique du 23 septembre 1978
CONSEIL SCIENTIFIQUE
FONDATION
STATUT
VISITEUR
RUSSE
CHINOIS
SEMINAIRE
PHYSIQUE THEORIQUE
UNESCO
PHYSICIEN
BIBLIOTHEQUE
PUBLICATIONS MATHEMATIQUES
RESIDENCE ORMAILLE
BOIS-MARIE
PARC
INFORMATIQUE
ORDINATEUR
FINANCEMENT
H1.1.4.6.3/3
IHES
04/12/1978
21x29,7
5 f.
FR
TEXTE
RAPPORT
H1_1_4_6_3_3.pdf
1978