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The principal aim of this article is to establish an iteration method on thespace of resurgent functions. We discuss endless continuability of iteratedconvolution products of resurgent functions and derive their estimatesdeveloping the method in arXiv:1610.05453. Using the estimates, we show theresurgence of formal series solutions of nonlinear differential and differenceequations.

Resurgent functions and nonlinear systems of differential and difference equations