标题： 倾斜型IV和VIIh Bianchi模型的未来渐近行为 显示英文标题

标题： Future Asymptotic Behaviour of Tilted Bianchi models of type IV and VIIh

摘要： 使用动力系统理论和详细的数值分析，研究了类型IV和VII$_h$的倾斜完美流体Bianchi模型的晚期行为。 特别是研究了真空平面波时空，并讨论了一个重要结果，即对于非膨胀流体，唯一的未来吸引平衡点是Bianchi类型VII$_h$模型中的平面波解。 在Bianchi类型IV模型中，参数空间的一个微小区域（漏洞）被显示包含一个闭合轨道，该轨道被发现作为吸引子（ Mussel吸引子）。 从广泛的数值分析中发现，晚期时归一化的能量密度趋于零，归一化变量“冻结”到它们的渐近值。 然后对类型VII$_h$模型进行详细数值分析，显示在参数空间中存在一个开集，其中解曲线趋近于一个拓扑为环面的紧致表面。 显示英文摘要

摘要： Using dynamical systems theory and a detailed numerical analysis, the late-time behaviour of tilting perfect fluid Bianchi models of types IV and VII$_h$ are investigated. In particular, vacuum plane-wave spacetimes are studied and the important result that the only future attracting equilibrium points for non-inflationary fluids are the plane-wave solutions in Bianchi type VII$_h$ models is discussed. A tiny region of parameter space (the loophole) in the Bianchi type IV model is shown to contain a closed orbit which is found to act as an attractor (the Mussel attractor). From an extensive numerical analysis it is found that at late times the normalised energy-density tends to zero and the normalised variables 'freeze' into their asymptotic values. A detailed numerical analysis of the type VII$_h$ models then shows that there is an open set of parameter space in which solution curves approach a compact surface that is topologically a torus.