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Abstract : The property, for quasiperiodic structures built by the cut and project or any equivalent method, to be related to a periodic lattice by a bounded deformation is a strong restriction on the window defining the strip, or on the atomic surface. We give a sufficient condition which is also necessary in one dimension for the existence of such a bounded modulation to a lattice which requires that the window tiles the orthogonal space. Using a special procedure we extend our proof to more general, albeit still non generic, situations including tilings of the Penrose type.

Mots-clés : displacive transformations quasicrystals





Author: Michel Duneau Christophe Oguey

Source: https://hal.archives-ouvertes.fr/



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