体粘性宇宙学中的退化Bogdanov-Takens分支
Degenerate Bogdanov-Takens bifurcations in a bulk viscous cosmology
摘要：
利用动力学系统理论证明了在宇宙学常数存在的情况下，具有体粘滞流体的Friedmann-Robertson-Walker（FRW）宇宙学模型等价于一个退化的二维Bogdanov-Takens规范形.状态方程参数$ω$、体粘滞系数$ξ$和宇宙学常数$Λ$定义了展开简并Bogdanov-Takens系统的必要参数。讨论了系统的不动点及其稳定性随相关参数$ω$、$Λ$和$ξ$的变化。稳定性的变化可视化适当的分歧图。给出了有限域相图和整体相图，讨论了结构稳定性问题。典型的问题，如后期加速或膨胀，可以引起的粘度，并可能有相关的观测宇宙学进行了讨论。
英文摘要：
Using the dynamical system theory we show that the Friedmann-Robertson-Walker (FRW) cosmological model with bulk viscous fluid in the presence of cosmological constant is equivalent to a degenerate two dimensional Bogdanov-Takens normal form. The equation of state parameter, $ω$, the bulk viscosity coefficient, $ξ$, and the cosmological constant, $Λ$, define the necessary parameters for unfolding the degenerate Bogdanov-Takens system. The fixed points of the system are discussed together with the variation of their stability properties upon changing the relevant parameters $ω$, $Λ$ and $ξ$. The variation of the stability properties are visualized by the appropriate bifurcation diagrams. Phase portrait for finite domain and global phase portrait are displayed and the issue of the structural stability is discussed. Typical issues such as late acceleration or inflation that can be induced by viscosity and could have relevance to observational cosmology are also discussed.
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