  We obtain general results on the dynamics of exactly conical geometries,
where we use the notion of boundaries at infinity to characterize asymptotic
behavior. As we demonstrate in examples, these notions also apply to smooth
geometries that are merely asymptotically conical, such as the Eguchi-Hanson or
resolved conifold geometries. In these cases we obtain a rather complete
qualitative understanding of the varieties of asymptotic behavior, and we probe
the connectivity of the phase space by finding infinitely large families of
multiple geodesics connecting a point on the infinite past boundary with a
point in the infinite future boundary.
