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Resurgence relations for classes of differential and difference equations. (English) Zbl 1078.34068
The paper is devoted to the study of meromorphic differential and difference equations of level 1. It is shown that small solutions of these equations can be represented as exponential series with Borel sums of certain formal series as coefficients. The Stokes transition in these representations is considered in the case that the sum of the coefficients is changed between sectors. Finally, resurgence relations are derived by using one-sided Borel transforms and a sketch is given of the bridge equation of Ecalle and its use for the above-mentioned equations.

MSC:
34M25 Formal solutions and transform techniques for ordinary differential equations in the complex domain
34M37 Resurgence phenomena (MSC2000)
39A10 Additive difference equations
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References:
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