Perturbation Theory for Systems without Global Action-Angle Coordinates
Hamiltonian perturbation theory is usually formulated with reference to systems defined in a product space B × T m endowed with a system of action-angle coordinates I ∈ B,φ ∈ T m , where B is an open set in R m . This is essentially a ‘local’ formulation since the phase space of an integrable Hamiltonian system can easily fail to have such a product structure in the large, and correspondingly there exists no single ‘global’ system of action-angle coordinates.
KeywordsNormal Form Action Space Hamilton Function Invariant Tori Integrable Hamiltonian System
Unable to display preview. Download preview PDF.
- Benettin, G., and Fassò, F., 1993, Paper in preparation.Google Scholar
- Cushman, R., 1984, Normal form for hamiltonian vectorfields with periodic flow, in Differential Geometric Methods in Mathematical Physics, S. Sternberg ed., Reidel, Dordrecht.Google Scholar
- Cushman, R., and Knörrer, H., 1985, The energy-momentum mapping of the Lagrange top, in Differential Geometric Methods in Mathematical Physics, H.D. Doebner and J.D. Henning eds., Lect. Notes Math. No. 1139, Springer Verlag, Berlin.Google Scholar
- Fassò, F., 1991, Fast Rotations of the Rigid Body and Hamiltonian Perturbation Theory. Ph.D. Thesis, SISSA, Trieste.Google Scholar
- Fassò, F., 1993, Geometry of the symmetric Euler-Poinsot system and Hamiltonian perturbation theory on a manifold. Preprint, University of Trento.Google Scholar