论文标题
叶状空间和伪群的混乱
Chaos for foliated spaces and pseudogroups
论文作者
论文摘要
我们将“对初始条件的敏感性”概括为叶的空间和伪群，在这种情况下提供了Devaney混乱的定义。与群体作用的情况相反，敏感性来自Devaney混乱的其他两个条件，我们表明这仅适用于紧凑型叶状空间，在非紧凑型情况下表现出反例。最后，我们获得了Auslander-Yorke二分法的类似物，用于紧凑的叶状空间和紧凑的假群。
We generalize "sensitivity to initial conditions" to foliated spaces and pseudogroups, offering a definition of Devaney chaos in this setting. In contrast to the case of group actions, where sensitivity follows from the other two conditions of Devaney chaos, we show that this is true only for compact foliated spaces, exhibiting a counterexample in the non-compact case. Finally, we obtain an analogue of the Auslander-Yorke dichotomy for compact foliated spaces and compactly generated pseudogroups.
