Bifurcation from the Kurth solution in galactic dynamics

Abstract

It will be shown that there exists an infinite-dimensional continuum $\mathcal{C}$ of weak static solutions of the Vlasov-Poisson system that bifurcates from the Kurth solution. Each $f_{\ast }\in \mathcal{C}$ has the charge density $\ddot{I}{}_{f_{\ast }}=\ddot{I}{}_{\mathrm{Kurth}}$, and (like the Kurth solution itself) each $f_{\ast }$ is surrounded by time-periodic weak solutions.