标题： 振荡类时奇点：Bianchi类型$\mathrm{VI}_{-1/9}$真空模型 显示英文标题

标题： Oscillatory spacelike singularities: The Bianchi type $\mathrm{VI}_{-1/9}$ vacuum models

摘要： 比安基类型$\mathrm{VI}_{-1/9}$、$\mathrm{VIII}$和$\mathrm{IX}$的真空模型都有4维的哈勃归一化状态空间，并预期具有一般的初始振荡奇点，但导致振荡的不变边界集对于类型$\mathrm{VI}_{-1/9}$来说比类型$\mathrm{VIII}$和$\mathrm{IX}$的要复杂得多。 首次，我们明确求解了这些类型$\mathrm{VI}_{-1/9}$边界集上的方程，并引入了一种新的图表示方法来描述相关的异宿链网络（即描述振荡的解序列）。 特别是，我们给出了纠缠循环异宿链网络的例子，并表明只有其中一些循环异宿链在渐近意义上是相关的。 显示英文摘要

摘要： The Bianchi type $\mathrm{VI}_{-1/9}$, $\mathrm{VIII}$ and $\mathrm{IX}$ vacuum models all have 4-dimensional Hubble-normalized state spaces and are expected to have a generic initial oscillatory singularity, but the invariant boundary sets responsible for the oscillations are much more complicated for type $\mathrm{VI}_{-1/9}$ than those of type $\mathrm{VIII}$ and $\mathrm{IX}$. For the first time, we explicitly solve the equations on these type $\mathrm{VI}_{-1/9}$ boundary sets and also introduce a new graph representation of the associated network of heteroclinic chains (i.e. sequences of solutions describing the oscillations). In particular, we give examples of networks of entangled cyclic heteroclinic chains and show that only some of these cyclic heteroclinic chains are asymptotically relevant.