Reference systems for splitting of separatrices

DOI10.1088/0951-7715/10/1/012zbMath0909.70019OpenAlexW2086834502MaRDI QIDQ3841274

Vassili Gelfreich

Publication date: 16 August 1998

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/5812c03c9ae73450f3033d003574df742e449e5c

zbMATH Keywords

small parametersplitting of invariant manifoldsexponentially small splittingcomplex phase spacehigh-frequency time-periodic perturbation

Mathematics Subject Classification ID

Hamilton's equations (70H05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

Related Items (12)

Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity. I ⋮ Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity. II: The generic case ⋮ Breakdown of homoclinic orbits to \(L_3\) in the RPC3BP. I: Complex singularities and the inner equation ⋮ Exponentially small splitting for the pendulum: A classical problem revisited ⋮ Chaotic layer of a nonlinear resonance driven by quasiperiodic perturbation. ⋮ Resurgence in a Hamilton-Jacobi equation. ⋮ Width of stochastic layers in near-integrable two-dimensional symplectic maps. ⋮ Analytic invariants for the \(1 : - 1\) resonance ⋮ Exponentially small splitting of separatrices beyond Melnikov analysis: Rigorous results ⋮ The width of a chaotic layer ⋮ Lyapunov exponents in resonance multiplets ⋮ A field theory approach to Lindstedt series for hyperbolic tori in three time scales problems

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