General Jacobi coordinates and Herman resonance for some nonheliocentric celestial \(N\)-body problems

DOI10.1134/S1560354720020021zbMath1480.70019OpenAlexW3016048546MaRDI QIDQ1987316

Chjan C. Lim

Publication date: 14 April 2020

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354720020021

zbMATH Keywords

perturbation theorycelestial \(N\)-body problemsgeneral Jacobi coordinatesHerman resonances

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) (n)-body problems (70F10)

Cites Work

• Unnamed Item
• Properly-degenerate KAM theory (following V. I. Arnold)
• The planetary \(N\)-body problem: symplectic foliation, reductions and invariant tori
• Relative periodic solutions of the \(N\)-vortex problem via the variational method
• Existence of KAM tori in the phase-space of lattice vortex systems
• Binary trees, symplectic matrices and the Jacobi coordinates of celestial mechanics
• On a strange resonance noticed by M. Herman
• Partial reduction in the \(N\)-body planetary problem using the angular momentum integral
• Stability of the planetary three-body problem. I: Expansion of the planetary Hamiltonian
• A combinatorial perturbation method and Arnold's whiskered tori in vortex dynamics
• Elimination of the nodes in problems ofn bodies
• Démonstration du ‘théorème d'Arnold’ sur la stabilité du système planétaire (d'après Herman)
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS
• Regularization of kepler's problem and the averaging method on a manifold

This page was built for publication: General Jacobi coordinates and Herman resonance for some nonheliocentric celestial \(N\)-body problems