The steep Nekhoroshev's theorem and optimal stability exponents (an announcement)

DOI10.4171/RLM/679zbMath1326.37040arXiv1403.6776MaRDI QIDQ467377

Giancarlo Benettin, Luigi Chierchia, Massimilliano Guzzo

Publication date: 3 November 2014

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.6776

zbMATH Keywords

steepnessHamiltonian systemsNekhoroshev's theoremresonant and non-resonant regions

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (6)

The Nekhoroshev theorem and the observation of long-term diffusion in Hamiltonian systems ⋮ Nekhoroshev's estimates for quasi-periodic time-dependent perturbations ⋮ Semi-analytic computations of the speed of Arnold diffusion along single resonances in a priori stable Hamiltonian systems ⋮ Quasi-effective stability for nearly integrable Hamiltonian systems ⋮ On steepness of 3-jet non-degenerate functions ⋮ The steep Nekhoroshev's theorem

Cites Work

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• AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
• Complex analysis and convolution operators
• Exponential stability for small perturbations of steep integrable Hamiltonian systems
• Prevalence of exponential stability among nearly integrable Hamiltonian systems
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