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The linearized Vlasov equation that governs the oscillations of a flat collision less stellar disk is integrated in action-angle variables, and the Poisson equation is solved exactly by use of a logarithmicspiral representation for the surface densities and potentials. An integral equation for the potential of unstable modes is derived, as well as small-amplitude conservation theorems for angular momentum and energy. A necessary and sufficient condition for the stability of axisymmetric disturbances is derived.
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Agris J. Kalnajs (1971) studied this question.
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