A new proof of the Bianchi type IX attractor theorem
A new proof of the Bianchi type IX attractor theorem
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Bianchi IX型吸引子定理的新证明
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
C. Uggla
中科院分区：
文献类型：
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作者：
J. Heinzle;C. Uggla
我们考虑了具有线性状态方程的Bianci IX型真空和正交理想流体模型的初奇性动力学。比安奇第九类吸引子定理指出，一般第九类解过去的渐近行为是由比安奇第一类和第二类真空态(Mixmaster吸引子)决定的。我们给出了这一定理的一个比较简短和完备的新证明。我们给出的证明本身很有趣，但更重要的是，它说明并强调了类型IX是特殊的，当人们考虑没有对称性的一般模型的更广泛的背景时，它在一定程度上具有误导性。
We consider the dynamics toward the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. The ‘Bianchi type IX attractor theorem’ states that the past asymptotic behavior of generic type IX solutions is governed by Bianchi type I and II vacuum states (Mixmaster attractor). We give a comparatively short and self-contained new proof of this theorem. The proof we give is interesting in itself, but more importantly it illustrates and emphasizes that type IX is special, and to some extent misleading when one considers the broader context of generic models without symmetries.