Small denominators and exponential stability: From Poincaré to the present time

DOI10.1007/BF02925829zbMath1024.37039MaRDI QIDQ4429202

Antonio Giorgilli

Publication date: 24 September 2003

Published in: Rendiconti del Seminario Matematico e Fisico di Milano (Search for Journal in Brave)

zbMATH Keywords

exponential stabilitysmall denominatorsclassical perturbation theorythree bodies problem

Mathematics Subject Classification ID

Three-body problems (70F07) 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) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)

Related Items (3)

Packets of resonant modes in the Fermi-Pasta-Ulam system ⋮ Kolmogorov algorithm for isochronous Hamiltonian systems ⋮ Avoiding Small Denominator Problems by Means of the Homotopy Analysis Method

Cites Work

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• On the stability of the Lagrangian points in the spatial restricted problem of three bodies
• Stability of motions near resonances in quasi-integrable Hamiltonian systems
• Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem
• On the problem of stability for near to integrable Hamiltonian systems
• Exponential stability for time dependent potentials
• Twistless KAM tori
• The Nekhoroshev theorem and the asteroid belt dynamical system
• Invariant KAM tori and global stability for Hamiltonian systems
• Kolmogorov theorem and classical perturbation theory
• Superexponential stability of KAM tori.
• On a connection between KAM and Nekhoroshev's theorems
• Compensations in small divisor problems
• Convergent series expansions for quasi-periodic motions
• Iteration of analytic functions
• On the Equilateral Configuration in the Restricted Problem of Three Bodies
• The Lagrange Configuration in Celestial Mechanics
• A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems
• Formal integrals for an autonomous Hamiltonian system near an equilibrium point
• AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
• Complex analysis and convolution operators
• METHODS FOR THE ANALYSIS OF THE LINDSTEDT SERIES FOR KAM TORI AND RENORMALIZABILITY IN CLASSICAL MECHANICS: A review with Some Applications
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS

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