Lipschitz classification of Bedford-McMullen carpets with uniform horizontal fibers

Abstract

Let ${\mathcal{M}}_{t,v,r}(n,m)$, $2\le m<n$, be the collection of self-affine carpets with expanding matrix $\diag(n,m)$ which are totally disconnected, possessing vacant rows and with uniform horizontal fibers. In this paper, we introduce a notion of structure tree of a metric space, and thanks to this new notion, we completely characterize when two carpets in ${\mathcal{M}}_{t,v,r}(n,m)$ are Lipschitz equivalent.

arXiv admin note: text overlap with arXiv:2005.07451

References in corpus (1)

• Lipschitz equivalence of self-similar sets and hyperbolic boundaries