论文标题
宇宙学全球动力系统分析
Cosmological global dynamical systems analysis
论文作者
论文摘要
我们考虑具有指数标量场的模型的动力系统公式，并在空间平坦和各向同性时空中具有线性状态方程式物质。与仅考虑线性双曲固定点分析的早期工作相反，我们对与分叉相关的非纤维固定点进行了中心歧管分析。但是，更重要的是，我们构建单调功能和DULAC功能。连同完整的局部固定点分析，这导致了描述这些模型的整个全局动态的证据，从而补充了文献中以前的局部结果。
We consider a dynamical systems formulation for models with an exponential scalar field and matter with a linear equation of state in a spatially flat and isotropic spacetime. In contrast to earlier work, which only considered linear hyperbolic fixed point analysis, we do a center manifold analysis of the non-hyperbolic fixed points associated with bifurcations. More importantly though, we construct monotonic functions and a Dulac function. Together with the complete local fixed point analysis this leads to proofs that describe the entire global dynamics of these models, thereby complementing previous local results in the literature.
