Liouville's equation. V. The full symmetries of r^-1-potentials

Details Liouville's equation. V. The full symmetries of r^-1-potentials Liouville's equation. V. The full symmetries of r^-1-potentials

Aug 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...275...91d&link_type=abstract

Astronomy and Astrophysics, Vol. 275, p. 91 (1993)

Astronomy and Astrophysics

Astrophysics

10

Galaxies, Dynamics And Evolution, Liouville'S Equation, Symmetries And Normal Modes

Scientific paper

A systematic study of the symmetries of Liouville's equation for r-1-potential is presented. The canonical transformations in phase space which leave the hamiltonian invariant turn out to be the full symmetry transformations of Liouville's operator, as well. The symmetry group is SO(4). A maximal set of mutually commuting operators, and subsequently, a classification of the eigensolutions of Liouville operator is proposed. The Kustaanheimo-Stiefel transformation is used to show that this SO(4) is isomorphic to a constrained SU(4) and contains all symmetries of Liouville's equation for r-1-potential.

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