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Resurgence of formal series solutions of nonlinear differential and difference equations. (English) Zbl 1354.34143

From the introduction and summary: This is an announcement of our forthcoming paper the main subject of which is the resurgence of the formal series solution of \[ {d\varphi\over dx}= F(x^{-1},\varphi), \] with \(F(x^{-1},\varphi)\in \mathbb{C}^n\{x^{-1},\varphi\}\) satisfying the conditons \[ F(0,0)= 0\quad\text{and}\quad \det(\partial_\varphi F(0,0))\neq 0. \] We derive an estimate for iterated convolution products. We describe the possible location of the singularities of their Borel transforms.

MSC:

34M30 Asymptotics and summation methods for ordinary differential equations in the complex domain
34M25 Formal solutions and transform techniques for ordinary differential equations in the complex domain
34M40 Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain
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