We define a class of dynamical systems by modifying a construction due to Tao, which includes certain Furstenburg limits arising from the Liouville function. Most recent progress on the Chowla conjectures and sign patterns of the Mobius and Liouville functions uses methods that apply to any dynamical system in this class. Hence dynamical systems in this class with anomalous local behavior present obstructions to further progress on these problems by the same techniques. We construct straightforward examples of dynamical systems in this class based on polynomial phases and calculate the resulting obstruction. This requires explicit bounds for the number of sign patterns arising in a certain way from polynomials, which is elementary but not completely trivial.

中文翻译：

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Liouville 和障碍物的动力学模型以进一步研究标志模式

我们通过修改由道引起的构造来定义一类动力系统，其中包括由刘维尔函数引起的某些弗斯滕堡极限。莫比乌斯函数和刘维尔函数的乔拉猜想和符号模式的最新进展使用的方法适用于此类中的任何动力系统。因此，此类具有异常局部行为的动力系统阻碍了通过相同技术进一步解决这些问题。我们基于多项式相位构建了此类中动态系统的简单示例，并计算了由此产生的障碍。这需要以某种方式从多项式中产生的符号模式数量的明确界限，这是基本的但并非完全无关紧要。