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Transseries for a class of nonlinear difference equations

Given a nonlinear analytic difference equation of level 1 with a formal power series solution ŷ 0 we associate with it a stable manifold of solutions with asymptotic expansion ŷ 0. This manifold can be represented by means of Borel summable series. All solutions with asymptotic expansion ŷ 0 in some sector can be written as certain exponential series which are called transseries. Some of their properties are investigated: are resurgence properties and Stokes transition. Analogous problems for differential equations have been studied by Costin in [7]