论文标题
在复杂的Shimizu中的双曲线吸引子上 - 莫里卡模型
On Hyperbolic Attractors in Complex Shimizu -- Morioka Model
论文作者
论文摘要
我们提出了一个经过修改的复合物值Shimizu-Morioka系统，具有均匀的双曲吸引子。庞加莱横截面中数值观察到的吸引子在拓扑上靠近Smale-Williams螺线管。由于相位空间的几何布置和附加的扰动项，因此复杂变量的论点经历了Bernoulli-Type图，对于Smale - Williams吸引子至关重要。鞍座平衡“散射”轨迹附近的相空间的转换向新角度，然后从鞍座延伸并返回下一个“散射”。我们提供了模型的数值模拟结果，并展示了Smale -Williams Type出现双曲线吸引子的典型特征。重要的是，我们在数值测试中显示了切线子空间的横向性 - 均匀双曲吸引子的关键特性。
We present a modified complex-valued Shimizu -- Morioka system with uniformly hyperbolic attractor. The numerically observed attractor in Poincaré cross-section is topologically close to Smale -- Williams solenoid. The arguments of the complex variables undergo Bernoulli-type map, essential for Smale -- Williams attractor, due to the geometrical arrangement of the phase space and an additional perturbation term. The transformation of the phase space near the saddle equilibrium "scatters" trajectories to new angles, then trajectories run from the saddle and return to it for the next "scatter". We provide the results of numerical simulations of the model and demonstrate typical features of the appearing hyperbolic attractor of Smale -- Williams type. Importantly, we show in numerical tests the transversality of tangent subspaces -- a pivotal property of uniformly hyperbolic attractor.
