标题： 高斯-博内引力中Bianchi IX宇宙的混沌动力学 显示英文标题

标题： Chaotic dynamics of the Bianchi IX universe in Gauss-Bonnet gravity

摘要： 我们研究了闭合FRW宇宙和由两个尺度因子表征的各向异性Bianchi型-IX宇宙在包含更高曲率（Gauss-Bonnet）项的引力理论中的动力学行为。 宇宙常数的存在在系统相空间中产生了一个鞍点类型的临界点。 从分隔线邻域开始的轨道将演化到临界点，并最终要么膨胀到de Sitter空间，要么坍缩到大挤压。 在闭合FRW模型中，动力学简化为二维中心流形中的双曲运动，系统不是混沌的。 在各向异性模型中，各向异性引入了旋转模式，该模式与双曲模式相互作用，在临界点附近呈现出不稳定周期轨道的圆柱结构。 由于系统的非可积性，旋转模式和双曲模式的相互作用使系统变得混沌，使得我们无法预测宇宙的最终命运。 我们发现，混沌动力学源于这样的事实：围绕分隔线的轨道在最终膨胀或坍缩之前会在临界点附近振荡。 吸引子的基域中的分形结构也证明了这种混沌特性。 显示英文摘要

摘要： We investigate the dynamics of closed FRW universe and anisotropic Bianchi type-IX universe characterized by two scale factors in a gravity theory including a higher curvature (Gauss-Bonnet) term. The presence of the cosmological constant creates a critical point of saddle type in the phase space of the system. An orbit starting from a neighborhood of the separatrix will evolve toward the critical point, and it eventually either expands to the de Sitter space or collapses to the big crunch. In the closed FRW model, the dynamics is reduced to hyperbolic motions in the two-dimensional center manifold, and the system is not chaotic. In the anisotropic model, anisotropy introduces the rotational mode, which interacts with the hyperbolic mode to present a cylindrical structure of unstable periodic orbits in the neighborhood of the critical point. Due to the non-integrability of the system, the interaction of rotational and hyperbolic modes makes the system chaotic, making it impossible for us to predict the final fate of the universe. We find that the chaotic dynamics arises from the fact that orbits with even small perturbations around the separatrix oscillate in the neighborhood of the critical point before finally expanding or collapsing. The chaotic character is also evidenced by the fractal structures in the basins of attraction.