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Hamiltonian perturbation theory for numerically constructed phase-space tori

1994; Oxford University Press; Volume: 268; Issue: 4 Linguagem: Inglês

10.1093/mnras/268.4.1041

1365-2966

M. Kaasalainen,

Quantum, superfluid, helium dynamics

The methods of McGill & Binney and Kaasalainen & Binney are employed in creating invariant phase-space tori in non-integrable potentials supporting minor-orbit families. Following Binney & Kumar, these tori are used to define an integrable Hamiltonian H0 closely approximating the original one, and Hamiltonian perturbation theory is then used to demonstrate that a minor-orbit family can be treated as one made up of orbits trapped by a resonance of H0. The main objectives of this paper are (i) to develop a model for perturbative calculations, resembling the pendulum analysis of standard secular perturbation theory, that takes into account the special properties of H0, and (ii) to show how H0 may be constructed in the presence of powerful resonances, which render ineffective the approach of Binney & Kumar. As an illustration of the method, the ‘banana’ and ‘fish’ minor-orbit families in the planar logarithmic potential are explicitly derived by perturbing constructed H0s.