ISSN:
1572-9478
Keywords:
Dynamics
;
Hamiltonian systems
;
Keplerian systems
;
degeneracy
;
integrability
;
hydrogen atom
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract Deprit and Miller have conjectured that normalization of integrable Hamiltonians may produce normal forms exhibiting degenerate equilibria to very high order. Several examples in the class of coupled elliptic oscillators are known. In order to test the utility of normalization as a detector of integrability we normalize, to high order, a perturbed Keplerian system known to have several integrable limits; the generalized van der Waals Hamiltonian for a hydrogen atom. While the separable limits give rise to high order degeneracy we find a non-separable, integrable limit for which the normal form does not exhibit degeneracy. We conclude that normalization may, in certain cases, indicate integrability but is not guaranteed to uncover all integrable limits.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00051689
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