Bifurcation from the Kurth solution in galactic dynamics

TL;DR

This paper demonstrates the existence of an infinite-dimensional continuum of weak static solutions to the Vlasov-Poisson system that bifurcate from the Kurth solution, each sharing the same charge density and surrounded by time-periodic solutions.

Contribution

It establishes the bifurcation of a vast family of static solutions from the Kurth solution in galactic dynamics, expanding understanding of solution structures in the Vlasov-Poisson system.

Findings

Existence of an infinite-dimensional continuum of solutions.

Solutions share the same charge density as the Kurth solution.

Surrounded by time-periodic weak solutions.

Abstract

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