Functions of substitution tilings as a Jacobian

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A tiling τ of the Euclidean space gives rise to a function fτ, which is constant 1/ ITI on the interior of every tile T. In this paper we give a local condition to know when fτ, which is defined by a primitive substitution tiling of the Euclidean space, can be realized as a Jacobian of a biLipschitz homeomorphism of ℝd. As an example we show that this condition holds for any star-shaped substitution tiling of ℝ2. In particular, the result holds for any Penrose tiling.

Original languageEnglish
Pages (from-to)3853-3863
Number of pages11
JournalProceedings of the American Mathematical Society
Issue number11
StatePublished - 27 Aug 2013

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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