Passage Operators and Noncommutative Transfer of Integral Hyperbolicity in the Vlasov--Poisson System

We study variational transport along characteristics of a prescribed classical solution of the Vlasov--Poisson system with finite mass and a cosmological term. For transitions between transverse sections, we compute the differential of the transition map and establish an exact intertwining identity with the isochronous variational transport. We prove a sufficient cone criterion for finite-time hyperbolicity that persists under chronologically ordered compositions of transitions. The Poisson equation imposes a necessary restriction on the range of applicability of this criterion, and an explicit threshold is obtained in an exterior spherically symmetric field. We also establish a telescoping estimate for the averaged matrix and uniform bounds for products preserving a compatible family of positive-definite quadratic forms. For a three-dimensional submanifold of phase space, we study the loss of rank of its configuration-space projection.