The Falkner–Skan Equation II: Dynamics and the Bifurcations of P- and Q-Orbits

Abstract

The Falkner–Skan equation is a reversible three-dimensional system of ordinary differential equations with two distinguished straight-line trajectories which form a heteroclinic loop between fixed points at infinity. We showed in the previous paper (1995, J. Differential Equations119, 336–394) that at positive integer values of the parameter λ there are bifurcations creating large sets of periodic and other interesting trajectories. Here we show that all but two of these trajectories are destroyed in another sequence of bifurcations as λ→∞, and by considering topological invariants and orderings on certain manifolds we obtain unusually detailed information about the sequences of bifurcations which can occur.