二维分段光滑不可逆映射中锁模周期轨道到混沌的转变
Transition from mode-locked periodic orbit to chaos in a 2D piecewise smooth non-invertible map
摘要：
在这项工作中，我们报告了一个新的路线，从一个共振环面在一个分段光滑的不可逆映射的平面到自己的混沌。定义共振环面的闭不变曲线由鞍环的不稳定流形与稳定环和鞍环的点的并集构成。我们已经发现，一个尖点环面不能发展之前的混沌开始，虽然环环面出现。二维环面的破坏发生在不变曲线上存在无穷多个环的情况下，通过同宿分支。我们表明，由于不可逆的性质的地图，结构的吸引盆地的变化，从简单的连接到一个非连接的。我们还描述了如何过渡到混沌的机制不同的情况下出现的混沌可逆的地图，以及在光滑的不可逆的地图。
英文摘要：
In this work we report a new route to chaos from a resonance torus in a piecewise smooth non-invertible map of the plane into itself. The closed invariant curve defining the resonance torus is formed by the union of unstable manifolds of saddle cycle and the points of stable cycle and saddle cycle. We have found that a cusp torus cannot develop before the onset of chaos, though the loop torus appears. The destruction of the two-dimensional torus occurs through homoclinic bifurcation in the presence of an infinite number of loops on the invariant curve. We show that owing to the non-invertible nature of the map, the structure of the basin of attraction changes from simply connected to a nonconnected one. We also describe how the mechanism of transition to chaos differs from the scenario of appearance of chaos in invertible maps as well as in smooth non-invertible maps.
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