Normal forms à la Moser for aperiodically time-dependent Hamiltonians in the vicinity of a hyperbolic equilibrium

DOI10.3934/DCDSS.2016044zbMath1347.37109arXiv1503.05134OpenAlexW2123967129MaRDI QIDQ317111

Alessandro Fortunati, Stephen Wiggins

Publication date: 30 September 2016

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.05134

zbMATH Keywords

perturbation theoryintegrabilityHamiltonian systemsaperiodic time dependenceLie series method

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09)

Related Items (3)

A Theoretical Framework for Lagrangian Descriptors ⋮ Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations ⋮ Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium

Cites Work

• A Kolmogorov theorem for nearly integrable Poisson systems with asymptotically decaying time-dependent perturbation
• Exponential stability for time dependent potentials
• Persistence of Diophantine flows for quadratic nearly integrable Hamiltonians under slowly decaying aperiodic time dependence
• The analytic invariants of an area-preserving mapping near a hyperbolic fixed point
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