摘要：In this paper a 2-dimensional mapping is investigated in the complex field ℂ for the existence of analytic invariant curves. Employing the method of majorant series, we need to discuss the eigenvalue α of the mapping at a fixed point. Besides the hyperbolic case α ≠ 1 , we focus on those α on the unit circle S 1 , i.e., α = 1 . We discuss not only those α at resonance, i.e., at a root of the unity, but also those α near resonance under the Brjuno condition.
