Stability of the planetary three-body problem. II: KAM theory and existence of quasiperiodic motions
type: Item
instance of: scholarly article
title: Stability of the planetary three-body problem. II: KAM theory and existence of quasiperiodic motions
zbMATH Open document ID: 0837.70009
DOI: 10.1007/BF00692089
author: Philippe Robutel
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 1996-05-19T00:00:00Z
Mathematics Subject Classification ID: 70F07
Mathematics Subject Classification ID: 70F15
Mathematics Subject Classification ID: 37C75
zbMATH DE Number: 831532
zbMATH Keywords: KAM theory
zbMATH Keywords: Poincaré canonical elliptic variables
zbMATH Keywords: Arnold's theorem
zbMATH Keywords: existence of quasiperiodic orbits
zbMATH Keywords: degenerate cases
MaRDI profile type: Publication
cites work: PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
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cites work: Analysis of resonances in the spin-orbit problem in celestial mechanics. I: The synchronous resonance
cites work: Analysis of resonances in the spin-orbit problem in celestial mechanics. II: Higher order resonances and some numerical experiments
cites work: Construction of analytic KAM-surfaces and effective stability bounds
cites work: Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem
cites work: Q5829223
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cites work: Q3294369
cites work: Estimates in the Kolmogorov theorem on conservation of conditionally periodic motions
cites work: The separation of motions in systems with rapidly rotating phase
cites work: Chaotic Evolution of the Solar System
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description: scientific article; zbMATH DE number 831532