Normalization through invariants in \(n\)-dimensional Kepler problems

DOI10.1134/S1560354718040032zbMath1474.37067OpenAlexW2885649280WikidataQ129437254 ScholiaQ129437254MaRDI QIDQ1739521

Patricia Yanguas, Jesús F. Palacián, Kenneth R. Meyer

Publication date: 26 April 2019

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

Full work available at URL: https://doi.org/10.1134/s1560354718040032

zbMATH Keywords

KAM theoryregular reductionDelaunay coordinatesperturbed Keplerian problemsdegenerate HamiltoniansKepler HamiltonianKeplerian invariantsMoser regularizationperiodic and quasi-periodic motions

Mathematics Subject Classification ID

Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Two-body problems (70F05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Celestial mechanics (70F15) Dynamical systems in classical and celestial mechanics (37N05) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items

Reduced 4D oscillators and orbital elements in Keplerian systems: Cushman-Deprit coordinates, Persistence of Lagrange invariant tori at tangent degeneracy

Cites Work

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• Invariant tori in the lunar problem
• Families of canonical transformations by Hamilton-Jacobi-Poincaré equation. Application to rotational and orbital motion
• Invariant tori in Hamiltonian systems with high order proper degeneracy
• Constrained normalization of Hamiltonian systems and perturbed Keplerian motion
• Reduction of symplectic manifolds with symmetry
• On the global symmetry of the classical Kepler problem
• Doubly-symmetric periodic solutions of the spatial restricted three-body problem
• Monodromy in the hydrogen atom in crossed fields
• Normal forms for perturbed Keplerian systems.
• Decomposition of functions for elliptic orbits
• The Kepler problem. Group theoretical aspects, regularization and quantization, with application to the study of perturbations (incl. CD-ROM)
• Flow reconstruction and invariant tori in the spatial three-body problem
• Regular and singular reductions in the spatial three-body problem
• Dynamical groups and spherical potentials in classical mechanics
• Quasi‐Periodic Almost‐Collision Orbits in the Spatial Three‐Body Problem
• Periodic Solutions in Hamiltonian Systems, Averaging, and the Lunar Problem
• On the Geometry of the Kepler Problem
• A note on the existence of invariant punctured tori in the planar circular restricted three-body problem
• The constrained normal form algorithm
• A new family of periodic orbits for the restricted problem
• The elimination of the parallax in satellite theory
• Characteristic Classes. (AM-76)
• Virtual singularities in the artificial satellite theory
• Collisions of stars by oscillating orbits of the second kind
• Reduction, Brouwer's Hamiltonian, and the critical inclination
• Perturbation theory of Kepler motion based on spinor regularization.
• Canonical transformations depending on a small parameter
• Regularization of kepler's problem and the averaging method on a manifold
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem
• On the regularization of the Kepler problem
• Algorithms in invariant theory
• Averaging the planar three-body problem in the neighborhood of double inner collisions
• Canonical elements for collision orbits