Pendulum: separatrix splitting

Abstract

An exact expression for the determinant of the splitting matrix is derived: it allows us to analyze the asympotic behaviour needed to amend the large angles theorem proposed in Ann. Inst. H. Poincaré, B-60, 1, 1994. The asymptotic validity of Melnokov's formulae is proved for the class of models considered, which include polynomial perturbations.

30 pages, one figure

References in corpus (2)

• Reminiscences on science at I.H.E.S. A problem on homoclinic theory and a brief review
• Fast Arnold's diffusion in isochronous systems

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• Asymptotic Expansion of the Homoclinic Splitting Matrix for the Rapidly, Quasiperiodically, Forced Pendulum
• Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous results
• On small breathers of nonlinear Klein-Gordon equations via exponentially small homoclinic splitting
• Splitting of separatrices in the resonances of nearly integrable Hamiltonian Systems of one and a half degrees of freedom
• Fast Arnold Diffusion in three time scale systems