Number-theoretic positive entropy shifts with small centralizer and large normalizer

M. BAAKE, Á. BUSTOS, C. HUCK, M. LEMAŃCZYK, A. NICKEL
2020 Ergodic Theory and Dynamical Systems  
Higher-dimensional binary shifts of number-theoretic origin with positive topological entropy are considered. We are particularly interested in analysing their symmetries and extended symmetries. They form groups, known as the topological centralizer and normalizer of the shift dynamical system, which are natural topological invariants. Here, our focus is on shift spaces with trivial centralizers, but large normalizers. In particular, we discuss several systems where the normalizer is an
more » ... alizer is an infinite extension of the centralizer, including the visible lattice points and the k-free integers in some real quadratic number fields.
doi:10.1017/etds.2020.111 fatcat:dlva2cclk5gcrayizqukgrzq44