Analytic invariant curves for an iterative equation related to dissipative standard map

In this paper, we study existence of invariant curves of an iterative equation which is from dissipative standard map. By constructing an invertible analytic solution g (x ) of an auxiliary equation of the form invertible analytic solutions of the form g (λ g  ^? 1(x )) for the original iterative functional equation are obtained. Besides the hyperbolic case 0 < |λ | < 1, we focus on those λ on the unit circle S ¹, that is, |λ | = 1. We discuss not only those λ at resonance, that is, at a root of the unity, but also those λ near resonance under the Brjuno condition. Copyright © 2016 John Wiley & Sons, Ltd.