2025/01/05 by Rao, Hui, Xu, Yan-Li, Zhang, Yuan
#26A16 #28A80 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2501.02426
Doubling measure was introduced by Beurling and Ahlfors in 1956 and now it becomes a basic concept in analysis on metric space. In this paper, for a measure which is not doubling, we introduce a notion of point-wise doubling index, and calculate the point-wise doubling indices of uniform Bernoulli measures on Bedford-McMullen carpets. As an application, we show that, except a small class of Bedford-McMullen carpets, if two Bedford-McMullen carpets are bi-Lipschitz equivalent, then they have the same fiber sequence up to a permutation.