论文标题
复杂不稳定性的几何形状和四维符号图中的逃脱
Geometry of complex instability and escape in four-dimensional symplectic maps
论文作者
论文摘要
在四维符号地图中，周期性轨道的复杂不稳定性是可能的，在二维情况下不可能发生。我们研究了参数变化下固定点的稳定动力学到复杂的不稳定动力学的过渡。使用3D相空间切片和在频率空间中使用两个耦合标准地图的示例可视化常规结构的几何形状的变化。使用逃生时间情节和与复杂不稳定固定点相关的2D不变流形的计算来研究混乱的动力学。基于正常形式的描述，我们通过可视化逃生路径和复杂不稳定固定点周围的长期限制来研究潜在的运输机制。我们发现，逃生由沿正常形式不变平面的不稳定歧管的运输支配。
In four-dimensional symplectic maps complex instability of periodic orbits is possible, which cannot occur in the two-dimensional case. We investigate the transition from stable to complex unstable dynamics of a fixed point under parameter variation. The change in the geometry of regular structures is visualized using 3D phase-space slices and in frequency space using the example of two coupled standard maps. The chaotic dynamics is studied using escape time plots and by computations of the 2D invariant manifolds associated with the complex unstable fixed point. Based on a normal-form description, we investigate the underlying transport mechanism by visualizing the escape paths and the long-time confinement in the surrounding of the complex unstable fixed point. We find that the escape is governed by the transport along the unstable manifold across invariant planes of the normal-form.
