具有指数可积畸变的同胚下的维数压缩和展开

Pub Date : 2022-03-24 DOI:10.4310/arkiv.2022.v60.n2.a9

L. Hitruhin

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引用次数: 1

摘要

.我们改进了具有p-指数可积畸变的同胚的维数压缩和展开界。在第一个方向上，我们还引入了压缩多重分形谱的估计，它将用于估计维度的压缩，以及旋转多重分形谱。为了建立展开情况，我们使用逆映射的多重分形谱，并构造证明清晰度的例子。

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Dimension compression and expansion under homeomorphisms with exponentially integrable distortion

. We improve both dimension compression and expansion bounds for homeomorphisms with p -exponentially integrable distortion. To the ﬁrst direction we also introduce estimates for the compression multifractal spectra, which will be used to estimate compression of dimension, and for the rotational multifractal spectra. For establishing the expansion case we use the multifractal spectra of the inverse mapping and construct examples proving sharpness.

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