A Kolmogorov theorem for nearly integrable Poisson systems with asymptotically decaying time-dependent perturbation

DOI10.1134/S1560354715040061zbMath1353.70046arXiv1409.0430MaRDI QIDQ892768

Alessandro Fortunati, Stephen Wiggins

Publication date: 12 November 2015

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.0430

zbMATH Keywords

aperiodic time dependencePoisson systemsKolmogorov theorem

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Nearly integrable Hamiltonian systems, KAM theory (70H08)

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Cites Work

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• Nekhoroshev and KAM stabilities in generalized Hamiltonian systems
• Exponential stability for time dependent potentials
• Near-invariant tori on exponentially long time for Poisson systems
• Normal form and Nekhoroshev stability for nearly integrable Hamiltonian systems with unconditionally slow aperiodic time dependence
• Persistence of Diophantine flows for quadratic nearly integrable Hamiltonians under slowly decaying aperiodic time dependence
• Action-angle Coordinates for Integrable Systems on Poisson Manifolds
• STABLE AND OSCILLATING MOTIONS IN NONAUTONOMOUS DYNAMICAL SYSTEMS. A GENERALIZATION OF C. L. SIEGEL'S THEOREM TO THE NONAUTONOMOUS CASE