STABILITY OF NEARLY-INTEGRABLE SYSTEMS WITH DISSIPATION

DOI10.1142/S0218127413500363zbMath1270.37042arXiv1202.2443OpenAlexW2124314097MaRDI QIDQ2845155

Christoph Lhotka, Alessandra Celletti

Publication date: 22 August 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.2443

zbMATH Keywords

stabilitydissipative systemsresonant motion

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)

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Cites Work

• Normal form construction for nearly-integrable systems with dissipation
• On the stability of the Lagrangian points in the spatial restricted problem of three bodies
• Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem
• Exponential stability for time dependent potentials
• Nekhoroshev estimates for quasi-convex Hamiltonian systems
• Twistless KAM tori
• An application fo the Nekhoroshev theorem to the restricted three-body problem
• A pseudo-normal form for planar vector fields.
• Polynomial normal forms with exponentially small remainder for analytic vector fields
• Improved exponential stability for near-integrable quasi-convex Hamiltonians
• A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems
• AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS

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