标题： 渐近锥几何上的动力学 显示英文标题

标题： Dynamics on asymptotically conical geometries

摘要： 我们获得了关于精确锥形几何动力学的一般性结果，在这些结果中，我们利用无穷远边界的概念来刻画渐近行为。正如我们在例子中所展示的，这些概念同样适用于那些仅仅是渐近锥形的光滑几何，例如 Eguchi-Hanson 或解析锥形几何。在这些情况下，我们对各种渐近行为的种类有了相当完整的定性理解，并通过找到无穷多个连接无限过去边界上一点与无限未来边界上一点的多重测地线，探测了相空间的连通性。 显示英文摘要

摘要： 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.