Blue skies in the four body problem

Jason Mireles James
Department of Mathematical Sciences, Florida Atlantic University

Suppose that a 2 freedom Hamiltonian system has a saddle focus equilibrium solution. Moreover, assume that the attached stable/unstable manifolds intersect transversally in the energy level. In this case classic theorems of Henrard and Devaney describe the rich dynamics near the intersection. I'll recall the history of these homoclinic phenomena going back to the numerical work of Darwin, Moulton, and Stromgren in the early Twentieth Century. Then I'll discuss some more recent work on the equilateral restricted four body problem.