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Bounds, quadratic differentials and renormalization conjectures

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/SULLIVAN/1974-1995/M_91_25/M_91_25.pdf

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…

Mots-clés: 1991, ANALYSE VECTORIELLE, BELTRAMI, BLOHK, CAMPANINO, CANTOR, CARLESON, COULLET, DE MELO, DENJOY, DOUADY, EN, EPSTEIN, EUCLIDE, FEIGENBAUM, GROTZSCH, GUCKENHEIMER, HAUSDORF, HERMANN, HOLDER, HUBBARD, JAKOBSON, JOHNSON, JULIA, KOEBE, LANFORD, LIPSCHITZ, LYUBICH, MANDELBROT, MARKOV, MARTENS, MCMULLEN, MILNOR, PALUBA, PHYSIQUE, POINCARE, PREPUBLICATION, REICH, RENORMALISATION, RIEMANN, RUELLE, SCWARZ, SHARKOVSKI, STREBEL, SULLIVAN, SWIATEK, TEICHMULLER, TESSER, THEOREME DU POINT FIXE, THURSTON, VAN STRIEN, YOCCOZ, ZYGMUND

A Shorter proof of the existence of the Feigenbaum fixed point

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/LANFORD/1968-2013/M_84_39/M_84_39.pdf

Mots-clés: 1984, CAMPANINO, CVITANOVIC, DEMONSTRATION, EN, FEGENBAUM, LANFORD, LERAY, OPERATEURS NON LINAIRES, PREPUBLICATION, SCHAUDER, THEOREME DU POINT FIXE, TOPOLOGIE

Fixed points of composition operators

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/EPSTEIN/Depuis_1964/P_87_36/P_87_36.pdf

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…

Mots-clés: 1987, ANILE, CAMPANINO, CAUCHY, COLLET, COULLET, CVITANOVIC, DE LA LLAVE, DOUADY, ECKMANN, EN, EPSTEIN, FACOLINI, FEIGENBAUM, FRECHET, GALLAVOTTI, HERGLOTZ, HUBBARD, HURWITZ, JONKER, JULIA, KADANOFF, LANFORD, MESTEL, OPERATEURS DE COMPOSITION, OSTLUND, POINCARE, PREPUBLICATION, RAND, RUELLE, SCHAUDER, SCHWARZ, SETHNA, SHENKER, SIGGIA, SULLIVAN, THEOREME DU POINT FIXE, TIKHONOV, TOPOLOGIE, TRESSER, VITALI, WITTWER, ZWEIFEL

Analyticity properties of the Feigenbaum function

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/EPSTEIN/Depuis_1964/P_81_27/P_81_27.pdf

Absract : Analyticity properties of the Feigenbaum function [a solution ofg(x)=???1g(g(?x)) withg(0)=1,g?(0)=0,g?(0)

Mots-clés: 1981, CAMPANINO, COULLET, CVITANOVIC, DENJOY, DYNAMIQUE, EN, EPSTEIN, FEIGENBAUM, HERGLOTZ, HURWITZ, INFORMATIQUE QUANTIQUE, LANFORD, LASCOUX, PADE, PHYSIQUE STATISTIQUE, PREPUBLICATION, RESEAUX CEREBRAUX, RIEMANN, RUDIN, RUELLE, SCHWARZ, SYSTEMES COMPLEXES, THEORIES NON LINEAIRES, TRESSER, VALIRON, VITALI, WOLFF

On the existence of Fegeinbaum's fixed point

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/EPSTEIN/Depuis_1964/P_80_35/P_80_35.pdf

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 ?.

Mots-clés: 1980, ANALYSE FONCTIONNELLE, ASCOLI, BANACH, CAMPANINO, COLLET, DYNAMIQUE, ECKMANN, EN, EPSTEIN, FEIGENBAUM, FRECHET, KOCH, LANFORD, LIPSCHITZ, PHYSIQUE STATISTIQUE, PREPUBLICATION, RESEAUX CEREBRAUX, RUELLE, SCHAUDER, SCHWARZ, THEORIES NON LINEAIRES, VITALI