On the existence of fixed points of the composition operator for circle maps
type: Item
instance of: scholarly article
title: On the existence of fixed points of the composition operator for circle maps
zbMATH Open document ID: 0603.58004
DOI: 10.1007/BF01209392
published in: Communications in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: In the theory of circle maps with golden ratio rotation number formulated by \textit{M. T. Feigenbaum}, \textit{L. P. Kadanoff}, and \textit{S. I. Shenker} [Physica D 5, 370-386 (1982)], and by \textit{S. Ostlund}, \textit{D. Rand}, \textit{J. Sethna}, and \textit{E. Siggia} [ibid. 8, 303-342 (1983)], 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.
Mathematics Subject Classification ID: 58C30
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 3973875
zbMATH Keywords: golden ratio rotation number
zbMATH Keywords: composition operator
zbMATH Keywords: fixed points
zbMATH Keywords: wide range
author: Jean-Pierre Eckmann
author: Henri Epstein
MaRDI profile type: Publication
cites work: New proofs of the existence of the Feigenbaum functions
cites work: Analyticity properties of the Feigenbaum function
cites work: Universal properties of maps of the circle with \(\epsilon\)-singularities
cites work: Functional equations for circle homeomorphisms with golden ratio rotation number
cites work: Universal properties of the transition from quasi-periodicity to chaos in dissipative systems
description: scientific article; zbMATH DE number 3973875