由拉伸折叠和剪切混洗组合而成的混合和输送
Mixing and transport from combined stretching-and-folding and cutting-and-shuffling
摘要：
虽然控制示踪粒子的运输和混合的结构和分叉已被广泛研究的系统，只有拉伸和折叠，并在较小程度上为系统，只有切割和洗牌，很少有研究认为系统与两者的组合。我们证明了两个分叉的非混合岛与椭圆周期点，只发生在系统中相结合的切割和洗牌和拉伸和折叠，作为一个例子，使用一个地图近似双轴旋转的不到半满球形颗粒状。首先，我们刻画了椭圆岛包含的一个分支，从双曲周期点流形包含到切线包含。结果表明，非混合区的最大尺寸出现在分叉点处。我们还证明了一个分叉的周期点被湮灭的切割和洗牌行动。椭圆和双曲周期点的链，当围绕椭圆点的不变环面破裂时（根据Kolmogorov-Arnold-Moser（KAM）理论），当它们遇到切割线时可以湮灭。因此，庞加莱指数（光滑系统的拓扑不变量）不被保留。
英文摘要：
While structures and bifurcations controlling tracer particle transport and mixing have been studied extensively for systems with only stretching-and-folding, and to a lesser extent for systems with only cutting-and-shuffling, few studies have considered systems with a combination of both. We demonstrate two bifurcations for non-mixing islands associated with elliptic periodic points that only occur in systems with combined cutting-and-shuffling and stretching-and-folding, using as an example a map approximating biaxial rotation of a less-than-half-full spherical granular tumbler. First, we characterize a bifurcation of elliptic island containment, from containment by manifolds associated with hyperbolic periodic points to containment by cutting line tangency. As a result, the maximum size of the non-mixing region occurs when the island is at the bifurcation point. We also demonstrate a bifurcation where periodic points are annihilated by the cutting-and-shuffling action. Chains of elliptic and hyperbolic periodic points that arise when invariant tori surrounding an elliptic point break up [according to Kolmogorov-Arnold-Moser (KAM) theory] can annihilate when they meet a cutting line. Consequently, the Poincaré index (a topological invariant of smooth systems) is not preserved.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
