Scattering map for the Vlasov--Poisson system with a repulsive harmonic potential

Abstract

We consider the Vlasov--Poisson system with a repulsive harmonic potential and prove the (modified) scattering of solutions, as well as the existence of wave operators, in any spatial dimension $d\ge 2$. The main novelty of this work is the construction of the wave operators and the introduction of the lens transform for the Vlasov--Poisson system. In addition, we provide a new and simpler proof that relaxes the assumptions on the initial data compared with those in Bigorgne, Velozo Ruiz, and Velozo Ruiz (2025) and Velozo Ruiz, and Velozo Ruiz (2024).

25 pages