Normalization and the detection of integrability: The generalized van der Waals potential

DOI10.1007/BF00051689zbMath0819.70013MaRDI QIDQ1805151

David Farrelly, T. Uzer

Publication date: 27 August 1995

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

zbMATH Keywords

normal formshydrogen atomdegenerate equilibriaperturbed Keplerian systemintegrable limit

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Two-body problems (70F05) Atomic physics (81V45)

Related Items

First kind symmetric periodic solutions of the generalized van der Waals Hamiltonian, Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance, Isolated periodic orbits and stability in separable potentials, On the nonintegrability of the generalized van der Waals Hamiltonian system, Periodic orbits of Hamiltonian systems: applications to perturbed Kepler problems, Searching for integrable systems. An application of Kozlov theorem, Relative equilibria and bifurcations in the generalized van der Waals 4D oscillator, On the periodic structure of the anisotropic Manev problem

Uses Software

• Mathematica

Cites Work

• Constrained normalization of Hamiltonian systems and perturbed Keplerian motion
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• The spectrum of Jacobi matrices
• Painting the Phase Space Portrait of an Integrable Dynamical System
• On reduction of the four-dimensional harmonic oscillator
• Quantization of the conformal Kepler problem and its application to the hydrogen atom
• The symmetry group of the harmonic oscillator and its reduction
• Measuring Renyi dimensions by a modified box algorithm
• Perturbation theory of Kepler motion based on spinor regularization.
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