Analysis and Probability Seminar

We study the gravitational Vlasov-Poisson system which is used to describe the motion of galaxies and globular clusters. More specifically, we are concerned with the linear stability of so-called isochrone steady states. These have been introduced by the French mathematician and astronomer Michel Hénon and are characterized by the property that the period of a particle orbit only depends on its energy and is independent of its angular momentum. For this purpose, we define a suitable Hilbert space and operator, and then examine the spectrum of the operator. We follow a spectral-theory-based approach to show that the spectrum of the operator is purely essential and equal to $[0, \infty[$. This result seems to be promising for showing linear stability of isochrone steady states. The concepts of this talk are based on work by Mahir Hadžić, Gerhard Rein and Christopher Straub.