We focus on the complexity of a special flow built over an irrational rotation of the unit circle and under a roof function on the unit circle. We construct a weak mixing minimal special flow with bounded topological complexity. We also prove that if the roof function is \(C^\infty \), then the special flow has sub-polynomial topological complexity and the time one map meets the condition of Sarnak’s conjecture.

中文翻译：

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特殊流动，弱混合和复杂性

我们关注于在单位圆的非理性旋转上以及在单位圆上的屋顶函数下建立的特殊流程的复杂性。我们构造了具有有限拓扑复杂性的弱混合最小特殊流。我们还证明，如果屋顶函数为\（C ^ \ infty \），则该特殊流具有次多项式拓扑复杂度，并且一幅图满足Sarnak猜想的条件。