Existence of analytic invariant curves for a complex planar mapping near resonance
نویسنده
چکیده
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 S1, 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.
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