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.)

DOI10.5802/aif.1462zbMath0826.30004OpenAlexW2317164371MaRDI QIDQ1891888

David Sauzin

Publication date: 1 June 1995

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

Full work available at URL: http://www.numdam.org/item?id=AIF_1995__45_2_453_0

zbMATH Keywords

Hamilton-Jacobi equationdivergent seriesasymptotic analysisresurgencesplitting of separatricesalien derivations

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Singular perturbations for ordinary differential equations (34E15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) General summability methods (40C99) Series expansions of functions of one complex variable (30B99)

Related Items

Singular Separatrix Splitting and the Melnikov Method: An Experimental Study, Exponentially small splitting for the pendulum: A classical problem revisited, Stationary phase methods and the splitting of separatrices, Resurgence in a Hamilton-Jacobi equation., A new method for measuring the splitting of invariant manifolds, Exponentially small splitting of separatrices beyond Melnikov analysis: Rigorous results, An alternative method to estimate the splitting of separatrices for the discretized pendulum equation

Cites Work

• Singularities that are inaccessible by geometry
• An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum
• Transcendentally small transversality in the rapidly forced pendulum
• A multiplier theorem for Schrödinger operators
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