标题： 混沌退出到暴胀：暴胀前宇宙的动力学 显示英文标题

标题： Chaotic exit to inflation: the dynamics of pre-inflationary universes

摘要： 我们证明了带有物质和宇宙常数的各向异性 Bianchi 类型-IX 模型具有混沌动力学，这与相空间中鞍点中心的存在有关。 从鞍点中心周围的不稳定周期轨道发出的圆柱体的拓扑结构为模型中的混沌提供了不变表征。 该模型可以看作是描述膨胀早期阶段的模型，通向膨胀的方式是混沌的。 显示英文摘要

摘要： We show that anisotropic Bianchi type-IX models, with matter and cosmological constant have chaotic dynamics, connected to the presence of a saddle-center in phase space. The topology of cylinders emanating from unstable periodic orbits about the saddle-center provides an invariant characterization of chaos in the models. The model can be thought to describe the early stages of inflation, the way out to inflation being chaotic.