论文标题
排名一的奇怪吸引子与异性斜纹缠结
Rank-one strange attractors versus Heteroclinic tangles
论文作者
论文摘要
我们提出了一种在平面上定期扰动的微分方程家族中奇怪吸引子（可观察到的混乱）出现的机制。这两个参数是独立的，并在循环中连续马鞍的不变流形中以不同的方式起作用。当两个参数为零时，该流量表现出与两个均衡相关的吸引杂斜周期。第一个参数使循环中连续的马鞍的二维不变歧管拆开。第二力横向相交。这些相对位置可以使用Melnikov方法确定。 我们证明了两参数家族中许多复杂的动力学对象的存在，从支持SRB（西奈 - 荷利 - 鲍尔）措施到超级巨星的水槽和Hénon-type吸引者的“大型”奇怪吸引者的存在。我们绘制了与所考虑的问题相关的合理分叉图，并表明异斜缠结的发生是\ emph {prevalent}现象。
We present a mechanism for the emergence of strange attractors (observable chaos) in a two-parameter periodically-perturbed family of differential equations on the plane. The two parameters are independent and act on different ways in the invariant manifolds of consecutive saddles in the cycle. When both parameters are zero, the flow exhibits an attracting heteroclinic cycle associated to two equilibria. The first parameter makes the two-dimensional invariant manifolds of consecutive saddles in the cycle to pull apart; the second forces transverse intersection. These relative positions may be determined using the Melnikov method. Extending the previous theory on the field, we prove the existence of many complicated dynamical objects in the two-parameter family, ranging from "large" strange attractors supporting SRB (Sinai-Ruelle-Bowen) measures to superstable sinks and Hénon-type attractors. We draw a plausible bifurcation diagram associated to the problem under consideration and we show that the occurrence of heteroclinic tangles is a \emph{prevalent} phenomenon.
