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Analytic invariant curves for an iterative equation related to Pielou's equation

In this paper, we study the existence of analytic invariant curves of an iterative equation which is from Pielou's equation. By reducing the equation with the Schröder transformation to an auxiliary equation, the author discusses not only that the constant at resonance, i.e. at a root of the unity, but also those near resonance under the Brjuno condition.