Trajectory Structure in the Large

Abstract

In Section 5.5 the trajectories of φ were defined to be the maximal horizontal arcs. Locally they are the images, by a branch of the analytic mapping Φ ⁻¹, of the horizontal intervals in the w-plane. We are now going to represent the trajectory α through a regular point P ₀ in the large by this mapping. In this manner, we get α in its natural parametrization; moreover, as Φ ⁻¹ will be defined in a neighborhood of α, it also describes the relation between α and the neighboring trajectories.