Transseries for a class of nonlinear difference equations

Given a nonlinear analytic difference equation of level I with a formal power series solution (y) over cap (0) we associate with it a stable manifold of solutions with asymptotic expansion (y) over cap (0). This manifold can be represented by means of Borel summable series. All solutions with asymptotic expansion (y) over cap (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].