论文标题
不稳定的尺寸可变性，异二维循环和搅拌器以正常形式
Unstable dimension variability, heterodimensional cycles, and blenders in the border-collision normal form
论文作者
论文摘要
混沌吸引子通常包含具有不同维度不稳定的歧管的周期性解决方案。这允许双曲线吸引子无法进行动力学现象。这封信的目的是以边界碰撞正常形式证明这些现象。这是一个连续的，分段线性的地图家族，它在物理上相关，因为它捕获了在不同应用中的边境碰撞中产生的动态。由于地图是分段线性的，它们相对可与精确的分析相对舒适，并且我们能够明确识别异二维循环和搅拌机的参数值。对于单参数亚家族，我们通过不稳定的尺寸变异性确定涉及过渡的分叉。能够快速准确地计算周期性解决方案来促进这一点，并且分段线性形式应为进一步研究提供有用的测试床。
Chaotic attractors commonly contain periodic solutions with unstable manifolds of different dimensions. This allows for a zoo of dynamical phenomena not possible for hyperbolic attractors. The purpose of this Letter is to demonstrate these phenomena in the border-collision normal form. This is a continuous, piecewise-linear family of maps that is physically relevant as it captures the dynamics created in border-collision bifurcations in diverse applications. Since the maps are piecewise-linear they are relatively amenable to an exact analysis and we are able to explicitly identify parameter values for heterodimensional cycles and blenders. For a one-parameter subfamily we identify bifurcations involved in a transition through unstable dimension variability. This is facilitated by being able to compute periodic solutions quickly and accurately, and the piecewise-linear form should provide a useful test-bed for further study.
