Abstract: We briefly review various dynamical systems attached to a substitution and we discuss the relation between them. We also remind the concept of transversal of a dynamical system in our setting and for a particular one, we employ the symmetries induced by the substitution (and its geometric counterpart) to derive exact values of arbitrary patches in the tiling assigned to the substitution. It is known, that these frequencies are the values of the unique ergodic measure attached to the dynamical system. Then, we show how to use these results to say anything about the frequencies in the original, symbolic setting. We will illustrate the notions on examples, and the talk does not require any previous knowledge, except for basics of theory of dynamical systems and linear algebra.
From symbolic to geometric setting and back again - the renormalisation techniques for subshifts arising from primitive substitutions
27.11.2025 15:15 - 18:00
Organiser:
H. Bruin, R. Zweimüller
Location: