Tilings, substitution systems and dynamical systems generated by them
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.
KeywordsFinite Type Tiling System Derivation Tree Derivation Rule Substitution System
Unable to display preview. Download preview PDF.
- 1.R. Berger,The undecidability of the Domino Problem, Mem. Am. Math. Soc. No. 66 (1966).Google Scholar
- 2.W. H. Gottschalk and G. A. Hedlund,Topological Dynamics, Am. Math. Soc. Colloq. Publ., 1955.Google Scholar
- 3.J. C. Martin,Substitutional minimal flows, Am. J. Math.93 (1971).Google Scholar
- 4.J. C. Martin,Minimal flows arising from substitutions of non-constant length, Math. Systems. Theory7 (1973).Google Scholar
- 5.K. Petersen,Ergodic theory, Cambridge University Press, 1983.Google Scholar
- 6.R. Robinson,Undecidability and nonperidocity for tilings of the plane, Invent. Math.12 (1971).Google Scholar
- 7.H. Wang,Proving theorems by pattern recognition—II, Bell System Tech. J.40 (1961).Google Scholar