Tilings, substitution systems and dynamical systems generated by them
- Shahar Mozes
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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.
- 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).
- Tilings, substitution systems and dynamical systems generated by them
Journal d’Analyse Mathématique
Volume 53, Issue 1 , pp 139-186
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Shahar Mozes (1)
- Author Affiliations
- 1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel