Lipschitz classification of Bedford-McMullen carpets with uniform horizontal fibers

摘要

Let M-t,M-v,M-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 M-t,M-v,M-r (n, m) are Lipschitz equivalent.

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