论文标题
关于吸引套装家庭和收缩Lorenz吸引者的统计稳定性
On the statistical stability of families of attracting sets and the contracting Lorenz attractor
论文作者
论文摘要
我们介绍了使用相应生成的流量上的动态条件吸引矢量场的统计稳定性的标准。这些条件很容易通过已知的结果来验证所有奇异纤维吸引$ c^2 $向量场的集合，从而提供了统计上稳定的奇异吸引套件的强大示例（特别是洛伦兹和几何洛伦兹吸引者）。这些条件也证明可以依靠洛伦兹流动（也称为Rovella吸引子）的持久但不稳定的家族，提供了动态系统非开放家族成员的统计稳定性的例子。在这两种情况下，我们的条件都无法使用有关特殊选择的庞加莱部分的一维诱导动态扰动的详细信息。
We present criteria for statistical stability of attracting sets for vector fields using dynamical conditions on the corresponding generated flows. These conditions are easily verified for all singular-hyperbolic attracting sets of $C^2$ vector fields using known results, providing robust examples of statistically stable singular attracting sets (encompassing in particular the Lorenz and geometrical Lorenz attractors). These conditions are shown to hold also on the persistent but non-robust family of contracting Lorenz flows (also known as Rovella attractors), providing examples of statistical stability among members of non-open families of dynamical systems. In both instances, our conditions void the use of detailed information about perturbations of the one-dimensional induced dynamics on specially chosen Poincaré sections.
