Spectrum of the linearized Vlasov--Poisson equation around steady states from galactic dynamics

Abstract

We study the linearized Vlasov-Poisson equation in the gravitational case around steady states that are decreasing and continuous functions of the energy. We identify the absolutely continuous spectrum and give criteria for the existence of oscillating modes and estimate their number. Our method allows us to take into account an attractive external potential.

23 pages, 3 figures. v4: Introduction improved, references added, typos corrected. The main results are unchanged