Homogenization of Penrose tilings

Abstract

A homogenization theorem is proved for energies which follow the geometry of an a-periodic Penrose tiling. The result is obtained by proving that the corresponding energy densities are W 1 -almost periodic and hence also Besicovitch almost periodic, so that existing general homogenization theorems can be applied (Braides, 1986). The method applies to general quasicrystalline geometries. To cite this article: A. Braides et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).