Galactic Dynamics in the Siegel Half-Plane

G. Rosensteel
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G. Rosensteel: Tulane University, Physics Department

A chapter in Quantization, Coherent States, and Complex Structures, 1995, pp 271-279 from Springer

Abstract: Abstract 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.

Keywords: Coset Space; Angular Momentum Vector; Matrix Differential Equation; Isospectral Deformation; Inertia Ellipsoid (search for similar items in EconPapers)
Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-1060-8_31

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DOI: 10.1007/978-1-4899-1060-8_31

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