On the existence of fixed points of the composition operator for circle maps (Q1082659)

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.