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
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
Bounded structure of infinitely renormalizable mappings
GEOMETRIE COMBINATOIRE
RIGIDITE
SULLIVAN
M/89/45
IHES
07/1989
A4
6 f.
EN
TEXTE
PREPUBLICATION
M_89_45.pdf
1989