Resurgence in a Hamilton-Jacobi equation.

DOI10.5802/aif.1977zbMath1077.34086OpenAlexW99744796MaRDI QIDQ1415565

David Sauzin, Carme Olivé, Teresa M. Seara

Publication date: 8 December 2003

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2003__53_4_1185_0

zbMATH Keywords

Hamilton-Jacobi equationBorel summationresurgencesplitting of separatrices

Mathematics Subject Classification ID

Hamilton-Jacobi equations in mechanics (70H20) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30)

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Cites Work

• Singularities that are inaccessible by geometry
• An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum
• First steps in ``calcul étrange
• Résurgence d'un thème de Huygens-Fresnel. (The resurrection of a topic of Huygens-Fresnel)
• Splitting of separatrices for a pendulum with rapidly oscillating suspension point
• Résurgence paramétrique et exponentielle petitesse de l'écart des séparatrices du pendule rapidement forcé. (Parametric resurgence and exponential smallness of the splitting of the separatrices of the rapidly forced pendulum.)
• Summability of divergent series
• Reference systems for splitting of separatrices
• Adiabatic Invariant of the Harmonic Oscillator, Complex Matching and Resurgence
• On the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems
• Borel summation and splitting of separatrices for the Hénon map
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