Liouville's equation. IV - The full symmetries of quadratic potentials

Details Liouville's equation. IV - The full symmetries of quadratic potentials Liouville's equation. IV - The full symmetries of quadratic potentials

Jun 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992a%26a...259..128s&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 259, no. 1, p. 128-133.

Astronomy and Astrophysics

Astrophysics

8

Liouville Theorem, Potential Theory, Quadratic Equations, Stellar Motions, Coordinate Transformations, Hamiltonian Functions

Scientific paper

A systematic study of the symmetries of Liouville's equation for an arbitrary potential is presented. The method is applied to the case of quadratic potentials. The symmetry group of the latter turns out to be GL(3, c) with the noncompact subgroup SL(3, c). The latter, in turn, has the subgroups SU(3), and SO(3), SO(3, 1) and SU(2, 1) of which the first two are compact and the last two noncompact. Finally, the largest compact and the largest noncompact subgroups of GL(3, c) are used to classify the eigenmodes of Liouville's equation for quadratic potentials.

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