We construct covering maps from infinite blowups of the$n$-dimensional Sierpinski gasket $SG_n$ to certain compactfractafolds based on $SG_n$. These maps are fractal analogs of theusual covering maps from the line to the circle. The constructionextends work of the second author in the case $n=2$, but adifferent method of proof is needed, which amounts to solving aSudoku-type puzzle. We can use the covering maps to define thenotion of periodic function on the blowups. We give acharacterization of these periodic functions and describe theanalog of Fourier series expansions. We study covering maps ontoquotient fractalfolds. Finally, we show that such covering mapsfail to exist for many other highly symmetric fractals.
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机译：我们构造了覆盖图，从$ n $维Sierpinski垫圈$ SG_n $的无限爆炸到基于$ SG_n $的某些紧致分形。这些图是从直线到圆的通常覆盖图的分形类似物。在$ n = 2 $的情况下，该构造扩展了第二作者的工作，但需要使用不同的证明方法，这相当于解决了数独类型的难题。我们可以使用覆盖图来定义爆破中周期函数的概念。我们给出了这些周期函数的特征，并描述了傅立叶级数展开的模拟。我们研究覆盖图到商分形上。最后，我们证明了这种覆盖贴图对于许多其他高度对称的分形均不存在。
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