Pascal-Adic变换的遍历定理的自相似修正
Self-Similar Corrections to the Ergodic Theorem for the Pascal-Adic Transformation
摘要：
设T是Pascal-adic变换。对任意可测函数g，考虑对遍历定理sum_{k=0} ^{j-1} g（T^k x）- j/l sum_{k=0} ^{l-1} g（T^k x）的修正.当被视为定义在{0，.，l-1}，我们证明了一个合适的函数类g，这些量，一旦适当的重整化，收敛到（部分）自仿射函数的图形。后者仅依赖于x的遍历分量，并且是所谓的Blancmange函数的变形。我们还简要介绍了与Conway递归10，000元序列的一系列作品的联系。
英文摘要：
Let T be the Pascal-adic transformation. For any measurable function g, we consider the corrections to the ergodic theorem sum_{k=0}^{j-1} g(T^k x) - j/l sum_{k=0}^{l-1} g(T^k x). When seen as graphs of functions defined on {0,...,l-1}, we show for a suitable class of functions g that these quantities, once properly renormalized, converge to (part of) the graph of a self-affine function. The latter only depends on the ergodic component of x, and is a deformation of the so-called Blancmange function. We also briefly describe the links with a series of works on Conway recursive $10,000 sequence.
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