Borel summation and splitting of separatrices for the Hénon map

Vassili Gelfreich; David Sauzin

Displaying similar documents to “Borel summation and splitting of separatrices for the Hénon map”

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.

Resurgence relations for classes of differential and difference equations

Boele Braaksma, Robert Kuik (2004)

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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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Resurgence of the Kontsevich-Zagier series

Ovidiu Costin, Stavros Garoufalidis (2011)

Annales de l’institut Fourier

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The paper is concerned with the resurgence of the Kontsevich-Zagier series $f (q) = \sum_{n = 0}^{\infty} (1 - q) \dots (1 - q^{n})$ We give an explicit formula for the Borel transform of the power series when $q = e^{1 / x}$ from which its analytic continuation, its singularities (all on the positive real axis) and the local monodromy can be manifestly determined. We also give two formulas (one involving the Dedekind eta function, and another involving the complex error function) for the right, left and median summation of the...

Brolin's theorem for curves in two complex dimensions

Charles Favre, Mattias Jonsson (2003)

Annales de l’institut Fourier

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Given a holomorphic mapping $f : ℙ^{2} \to ℙ^{2}$ of degree $d \geq 2$ we give sufficient conditions on a positive closed (1,1) current of $S$ of unit mass under which $d^{- n} f^{n *} S$ converges to the Green current as $n \to \infty$ . We also conjecture necessary condition for the same convergence.