Resurgence relations for classes of differential and difference equations

Boele Braaksma; Robert Kuik

Displaying similar documents to “Resurgence relations for classes of differential and difference equations”

Borel summation and splitting of separatrices for the Hénon map

Vassili Gelfreich, David Sauzin (2001)

Annales de l’institut Fourier

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We study two complex invariant manifolds associated with the parabolic fixed point of the area-preserving Hénon map. A single formal power series corresponds to both of them. The Borel transform of the formal series defines an analytic germ. We explore the Riemann surface and singularities of its analytic continuation. In particular we give a complete description of the “first” singularity and prove that a constant, which describes the splitting of the invariant manifolds, does not vanish....

Multisummability of formal power series solutions of nonlinear meromorphic differential equations

Boele L. J. Braaksma (1992)

Annales de l'institut Fourier

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In this paper a proof is given of a theorem of J. Écalle that formal power series solutions of nonlinear meromorphic differential equations are multisummable.

The return of the quartic oscillator. The complex WKB method

A. Voros (1983)

Annales de l'I.H.P. Physique théorique

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Analyzability in the context of PDEs and applications

Ovidiu Costin, Saleh Tanveer (2004)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Resurgence in a Hamilton-Jacobi equation

Carme Olivé, David Sauzin, Tere M. Seara (2003)

Annales de l’institut Fourier

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We study the resurgent structure associated with a Hamilton-Jacobi equation. This equation is obtained as the inner equation when studying the separatrix splitting problem for a perturbed pendulum via complex matching. We derive the Bridge equation, which encompasses infinitely many resurgent relations satisfied by the formal solution and the other components of the formal integral.