  Let a system of differential equations possess a saddle-node periodic orbit
such that every orbit in its unstable manifold is homoclinic, i.e. the unstable
manifold is a subset of the (global) stable manifold. We study several
bifurcation cases where the splitting of such a homoclinic connection causes
the Blue Sky Catastrophe, including the onset of complex dynamics. The birth of
an invariant torus or a Klein bottle is also described.

Dynamical Systems