Lipschitz classification of Bedford-McMullen carpets with uniform horizontal fibers

Ya-min Yang; Yuan Zhang

Lipschitz classification of Bedford-McMullen carpets with uniform horizontal fibers

Metric Geometry 2020-07-23 v1

Authors: Ya-min Yang , Yuan Zhang

Abstract

Let ${\cal M}_{t,v,r}(n,m)$ , $2\leq m<n$ , 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 ${\cal M}_{t,v,r}(n,m)$ are Lipschitz equivalent.

Keywords

self-affine carpets bedford-mcmullen carpets lipschitz equivalence structure tree metric space uniform horizontal fibers

Cite

@article{arxiv.2007.11397,
  title  = {Lipschitz classification of Bedford-McMullen carpets with uniform horizontal fibers},
  author = {Ya-min Yang and Yuan Zhang},
  journal= {arXiv preprint arXiv:2007.11397},
  year   = {2020}
}

Comments

arXiv admin note: text overlap with arXiv:2005.07451

Lipschitz classification of Bedford-McMullen carpets with uniform horizontal fibers

Abstract

Keywords

Cite

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