Scattered disc dynamics: the mapping approach

We derive, and discuss the properties of, a symplectic map for the dynamics of bodies on nearly parabolic orbits. The orbits are perturbed by a planet on a circular, coplanar orbit interior to the pericentre of the parabolic orbit. The map shows excellent agreement with direct numerical integrations and elucidates how the dynamics depends on perturber mass and pericentre distance. We also use the map to explore the onset of chaos, statistical descriptions of chaotic transport, and sticking in mean-motion resonances. We discuss implications of our mapping model for the dynamical evolution of the Solar system's scattered disc and other highly eccentric trans-Neptunian objects.