论文标题
可视化三维广义的Hénon地图的吸引子
Visualizing Attractors of the Three-Dimensional Generalized Hénon Map
论文作者
论文摘要
我们研究了通用二次差异性的动力学，这是平面Hénon图的3D概括。为了关注耗散性，定向保存案例，我们对编码词和两个分叉进行了全面的参数研究。周期性的轨道出生于Neimark-Sacker分叉的共鸣，在参数空间中引起了Arnold的舌头。上的吸引子包括不变的圆圈和混乱的轨道；这些以旋转数量和Lyapunov指数为特征。混乱的轨道包括类似于Hénon的和Lorenz的吸引子，这些吸引者可能是由于级联时期的级联反应而引起的，以及那些因不变圈的破坏而出生的。后者位于固定点的局部不稳定歧管附近的抛物面。
We study dynamics of a generic quadratic diffeomorphism, a 3D generalization of the planar Hénon map. Focusing on the dissipative, orientation preserving case, we give a comprehensive parameter study of codimension-one and two bifurcations. Periodic orbits, born at resonant, Neimark-Sacker bifurcations, give rise to Arnold tongues in parameter space. Aperiodic attractors include invariant circles and chaotic orbits; these are distinguished by rotation number and Lyapunov exponents. Chaotic orbits include Hénon-like and Lorenz-like attractors, which can arise from period-doubling cascades, and those born from the destruction of invariant circles. The latter lie on paraboloids near the local unstable manifold of a fixed point.
