scientific article; zbMATH DE number 549905

zbMath0792.34053MaRDI QIDQ4287414

Vassili Gelfreich

Publication date: 12 April 1994

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

asymptotic formulaPoincaré-Arnold-Melnikov methodrapidly forced pendulumseparatrices splitting angle

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Forced motions for nonlinear problems in mechanics (70K40) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Asymptotic expansions of solutions to ordinary differential equations (34E05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (10)

Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity. I ⋮ Exponentially small splitting for the pendulum: A classical problem revisited ⋮ Lower and upper bounds for the splitting of separatrices of the pendulum under a fast quasiperiodic forcing ⋮ Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems ⋮ On the role of high order resonances in normal forms and in separatrix splitting ⋮ Exponentially small splitting of separatrices beyond Melnikov analysis: Rigorous results ⋮ Exponentially small splitting of separatrices in a weakly hyperbolic case ⋮ Unnamed Item ⋮ Melnikov method and exponentially small splitting of separatrices ⋮ Exponentially small upper bounds for the splitting of separatrices for high frequency periodic perturbations

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