On the existence of Fegeinbaum's fixed point
RESEAUX CEREBRAUX
PHYSIQUE STATISTIQUE
ANALYSE FONCTIONNELLE
THEORIES NON LINEAIRES
DYNAMIQUE
Abstract : We give a proof of the existence of aC2, even solution of Feigenbaum's functional equation
g(x)=???10g(g(??0x)),g(0) = 1,
whereg is a map of [?1, 1] into itself. It extends to a real analytic function over ?.
EPSTEIN
CAMPANINO
P/80/35
IHES
1980
A4
38 f.
EN
TEXTE
PREPUBLICATION
P_80_35.pdf
1980
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
Confinement in Zn lattice Gauge theories implies confinement un SU(n) lattice Higgs theories : a New look at generalized, non-linear ?-models and Yang-Mills theory
THEORIES DES JAUGES
QUARKS
CHAMPS SCALAIRES
THEORIE DE YANG-MILLS
FROHLICH
P/79/02
IHES
02/1979
A4
15 f.
EN
TEXTE
PREPUBLICATION
P_79_02.pdf
1979
A Computer-assisted proof of the Feigenbaum conjectures
DEMONSTRATION
THEORIE DU CHAOS
INFORMATIQUE
LANFORD
P/81/17
IHES
04/1981
A4
7 f.
EN
TEXTE
PREPUBLICATION
P_81_17.pdf
1981
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
Compte-rendu du comité scientifique du 10 mars 1979
CONSEIL SCIENTIFIQUE
VISITEUR
SEMINAIRE
UNESCO
PUBLICATIONS SCIENTIFIQUES
ORDINATEUR
INFORMATIQUE
RESIDENCE ORMAILLE
BOIS-MARIE
TOUR
PARC
H1.1.4.7.1/2
IHES
05/04/1979
21x29,7
7 f.
FR
TEXTE
CORRESPONDANCE
H1_1_4_7_1_2.pdf
1979