Dynamical Systems seminar - B-free number-theoretical shift spaces and their symmetries

Dates

Wednesday, April 20, 2022 - 14:00 to 15:00

Speaker: Alvaro Bustos-Gajardo (The Open University)

Abstract: We discuss shift spaces constructed from indicator functions of number-theoretically defined sets, focusing mostly on their factorization properties (examples include the d-dimensional shift of visible lattice points and the family of k-free shift spaces coming from a finite field extension of Q). These subshifts exhibit interesting (and, from certain perspectives, unusual) properties, including the combination of high complexity (positive entropy) with symmetry rigidity (the automorphism group is “essentially trivial”, containing only shift maps). We will talk mostly about two-dimensional examples, focusing our discussion on the extended symmetry group, which is a mild generalization of the automorphism group which exhibits a wide variety of interesting behaviors in this context.