The Existence of Analytic Invariant Curves for a Planar Map
In this paper, we study the existence of analytic invariant curves for two-dimensional maps in the complex field C. Employing the method of majorant series, we discuss the eigenvalueof the mapping at a fixed point. We discuss not only thoseat resonance, i.e., at a root of the unity but also thosenear resonance under Brjuno condition.
Helen Zhang, Gang Shen and David Jin
L. X. Liu "The Existence of Analytic Invariant Curves for a Planar Map", Advanced Materials Research, Vols. 225-226, pp. 1274-1278, 2011