Analytic Invariant Curves for an Iterative Equation Related to Ricker-type Second-order Equation

In this paper, we consider the existence of analytic invariant curves of an iterative equation f(f(x))=xea−x−f(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(f(x)) = x{{\rm{e}}^{a - x - f(x)}}$$\end{document} which arises from Ricker-type second-order equation. By reducing the equation with the Schröder transformation to an auxiliary equation, the author discusses not only that the parameter at resonance, i.e., at a root of the unity, but also the parameter near resonance under the Brjuno condition.