FUNCTIONS OF SUBSTITUTION TILINGS AS A JACOBIAN

A tiling tau of the Euclidean space gives rise to a function f(tau), which is constant 1/vertical bar T vertical bar on the interior of every tile T. In this paper we give a local condition to know when f(tau), which is defined by a primitive substitution tiling of the Euclidean space, can be realized as a Jacobian of a biLipschitz homeomorphism of R-d. As an example we show that this condition holds for any star-shaped substitution tiling of R-2. In particular, the result holds for any Penrose tiling.