Substitution Tilings and Separated Nets with Similarities to the Integer Lattice

dc.creatorSolomon, Yaar
dc.date2008-10-29
dc.date2009-01-18
dc.date.accessioned2026-07-07T12:30:47Z
dc.date.available2026-07-07T12:30:47Z
dc.descriptionWe show that any primitive substitution tiling of the plane creates a separated net which is biLipschitz to the integer lattice. Then we show that if H is a primitive Pisot substitution in an Euclidean space, for every separated net Y, that corresponds to some tiling of the tiling space, there exists a bijection F between Y and the integer lattice that translate every element of Y a bounded distance. As a corollary we get that we have such an F for any separated net that corresponds to a Penrose Tiling. The proofs rely on results of Laczkovich, and Burago and Kleiner.
dc.identifierhttps://arxiv.org/abs/0810.5225
dc.identifierhttp://arxiv.org/abs/0810.5225
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216239
dc.subjectMetric Geometry
dc.subjectDynamical Systems
dc.titleSubstitution Tilings and Separated Nets with Similarities to the Integer Lattice
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