暗能量模型和中心流形的动力学
Dynamics of dark energy models and centre manifolds
摘要：
我们分析暗能量模型，其中自相互作用的三种形式或幻影场驱动宇宙的加速膨胀。这类模型的动力学经常通过重写宇宙学场方程的形式自治微分方程系统，或简单的动力学系统来研究。这些系统的性质通常通过线性稳定性理论来研究。在这种方法失败的情况下，例如由于雅可比矩阵中存在零特征值，可以应用中心流形理论。我们提出了一个简洁的介绍，并明确显示如何使用这个理论在两个具体的例子。
英文摘要：
We analyse dark energy models where self-interacting three-forms or phantom fields drive the accelerated expansion of the Universe. The dynamics of such models is often studied by rewriting the cosmological field equations in the form of a system of autonomous differential equations, or simply a dynamical system. Properties of these systems are usually studied via linear stability theory. In situations where this method fails, for instance due to the presence of zero eigenvalues in the Jacobian, centre manifold theory can be applied. We present a concise introduction and show explicitly how to use this theory in two concrete examples.
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