Abstract
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 language | American English |
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Pages (from-to) | 3853-3863 |
Number of pages | 11 |
Journal | Proceedings of the American Mathematical Society |
Volume | 141 |
Issue number | 11 |
DOIs | |
State | Published - 27 Aug 2013 |
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- General Mathematics