Galactic Dynamics in the Siegel Half-Plane

  • G. Rosensteel


The dynamics of rotating galaxies is modeled by a Hamiltonian Lax system for which the phase space is a homogeneous G-manifold with the Lie group G equal to either the noncompact real symplectic group Sp(n, R) or a maximal parabolic subgroup GCM(n). The dimensions n = 1, 2, 3 correspond respectively to breathing mode oscillations, planar rotations, and three-dimensional collective motion. The homogeneous GCM(3)-manifolds correspond to the Riemann ellipsoids. The homogeneous G-manifold Sp(n, R)/U(n), where U(n) is the maximal compact subgroup, is a classical complex domain diffeomorphic to the Siegel upper half-plane S n . Equilibrium galactic radii are determined for S 1 systems.


Coset Space Angular Momentum Vector Matrix Differential Equation Isospectral Deformation Inertia Ellipsoid 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • G. Rosensteel
    • 1
  1. 1.Physics DepartmentTulane UniversityNew OrleansUSA

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