论文标题
均匀自我措施及其应用的多重型光谱的不变性
Invariance of multifractal spectrum of uniform self-affine measures and its applications
论文作者
论文摘要
我们研究Bedford-McMullen地毯的Bi-Lipschitz分类，这些分类完全断开连接。让$ e $成为这样的地毯，让$μ_e$为$ e $的统一伯努利度量。我们表明，在Bi-Lipschitz地图下，$μ_e$的多重频谱和倍增属性都是不变的。此外，我们表明，如果$μ_e$和$μ_f$加倍，那么$ e $和$ f $之间的Bi-lipschitz地图享受一定的保留属性。
We study the bi-Lipschitz classification of Bedford-McMullen carpets which are totally disconnected. Let $E$ be a such carpet and let $μ_E$ be the uniform Bernoulli measure on $E$. We show that the multifractal spectrum and the doubling property of $μ_E$ are both invariant under a bi-Lipschitz map. Moreover, we show that if $μ_E$ and $μ_F$ are doubling, then a bi-Lipschitz map between $E$ and $F$ enjoys a certain measure preserving property.
