海森堡零流的时变混合
Mixing for Time-Changes of Heisenberg Nilflows
摘要：
我们考虑Heisenberg零流的重参数化。证明了如果海森堡零流是唯一遍历的，则光滑时变稠密子空间内的所有非平凡时变都是混合的。等价地，在特殊流的语言中，我们考虑了圆的无理旋转的线性斜移扩展上的特殊流。在不假设任何丢番图条件的频率，我们定义了一个密集类的光滑的屋顶功能，相应的特殊流量混合。混合是由一种称为伯克霍夫和拉伸的机制产生的。混合时变集（或等价地，混合屋顶函数）的补集具有可数余维，并且可以明确地用零流（或等价地，偏斜移位）的不变分布来描述，从而可以产生混合时变的具体例子。
英文摘要：
We consider reparametrizations of Heisenberg nilflows. We show that if a Heisenberg nilflow is uniquely ergodic, all non-trivial time-changes within a dense subspace of smooth time-changes are mixing. Equivalently, in the language of special flows, we consider special flows over linear skew-shift extensions of irrational rotations of the circle. Without assuming any Diophantine condition on the frequency, we define a dense class of smooth roof functions for which the corresponding special flows are mixing. Mixing is produced by a mechanism known as stretching of Birkhoff sums. The complement of the set of mixing time-changes (or, equivalently, of mixing roof functions) has countable codimension and can be explicitely described in terms of the invariant distributions for the nilflow (or, equivalently, for the skew-shift), allowing to produce concrete examples of mixing time-changes.
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