On the Existence of fixed points of the composition operator for circle maps

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/EPSTEIN/Depuis_1964/P_86_29/P_86_29.pdf

Epstein, Henri

EPSTEIN

05/1986

Abstract : In the theory of circle maps with golden ratio rotation number formulated by Feigenbaum, Kadanoff, and Shenker [FKS], and by Ostlund, Rand, Sethna, and Siggia [ORSS], a central role is played by fixed points of a certain composition operator in map space. We define a common setting for the problem of proving the existence of these fixed points and of those occurring in the theory of maps of the interval. We give a proof of the existence of the fixed points for a wide range of the parameters on which they depend.

RESEAUX CEREBRAUX

P/86/29

©IHES

Citer ce document

EPSTEIN et ECKMANN, “On the Existence of fixed points of the composition operator for circle maps,” Archives de l'IHES, consulté le 18 juin 2024, https://omeka.ihes.fr/document/P_86_29.pdf.