Lipschitz classification of Bedford-McMullen carpets with uniform horizontal fibers

Abstract

Let Mt,v,r(n, m), 2 ≤ 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 Mt,v,r(n, m) are Lipschitz equivalent.