Borel summability and Lindstedt series

DOI10.1007/s00220-006-0079-0zbMath1113.37047arXivmath-ph/0601032OpenAlexW2093430596MaRDI QIDQ883000

Guido Gentile, Alessandro Giuliani, Giovanni Gallavotti, Ovidiu Costin

Publication date: 31 May 2007

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0601032

zbMATH Keywords

quasi-periodic motionsperturbationsintegrable systemssum rulesKAM theoryhyperbolic toritwo-dimensional rotation vectors

Mathematics Subject Classification ID

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 (7)

BIFURCATION CURVES OF SUBHARMONIC SOLUTIONS AND MELNIKOV THEORY UNDER DEGENERACIES ⋮ Domains of analyticity and Lindstedt expansions of KAM tori in some dissipative perturbations of Hamiltonian systems ⋮ On parametric Gevrey asymptotics for some Cauchy problems in quasiperiodic function spaces ⋮ Quasiperiodic motions in dynamical systems: Review of a renormalization group approach ⋮ Quasi-periodic motions in strongly dissipative forced systems ⋮ Quasiperiodic Hamiltonian motions, scale invariance, harmonic oscillators ⋮ Gevrey estimates for asymptotic expansions of Tori in weakly dissipative systems*

Cites Work

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• Hyperbolic low-dimensional invariant tori and summations of divergent series
• Degenerate elliptic resonances
• An improvement of Watson’s theorem on Borel summability
• Majorant series convergence for twistless KAM tori
• Unicity of KAM tori

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