Abstract
The object of this work is to study the properties of dynamical systems defined by tilings. A connection to symbolic dynamical systems defined by one- and two-dimensional substitution systems is shown. This is used in particular to show the existence of a tiling system such that its corresponding dynamical system is minimal and topological weakly mixing. We remark that for one-dimensional tilings the dynamical system always contains periodic points.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Berger,The undecidability of the Domino Problem, Mem. Am. Math. Soc. No. 66 (1966).
W. H. Gottschalk and G. A. Hedlund,Topological Dynamics, Am. Math. Soc. Colloq. Publ., 1955.
J. C. Martin,Substitutional minimal flows, Am. J. Math.93 (1971).
J. C. Martin,Minimal flows arising from substitutions of non-constant length, Math. Systems. Theory7 (1973).
K. Petersen,Ergodic theory, Cambridge University Press, 1983.
R. Robinson,Undecidability and nonperidocity for tilings of the plane, Invent. Math.12 (1971).
H. Wang,Proving theorems by pattern recognition—II, Bell System Tech. J.40 (1961).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mozes, S. Tilings, substitution systems and dynamical systems generated by them. J. Anal. Math. 53, 139–186 (1989). https://doi.org/10.1007/BF02793412
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02793412