Automorphisms and extended symmetries of number-theoretic positive entropy subshifts.

ABSTRACT: We will discuss one- and multidimensional subshifts constructed via number-theoretically defined subsets of the integers (e.g. the visible lattice points in the plane, k-free integers, etc.), focusing our interest on their groups of automorphisms and extended symmetries, which are naturally defined conjugacy invariants. This type of shift space exhibits symmetry rigidity (that is, its group of automorphisms is essentially trivial), but is compatible with positive entropy and shows interesting variations on their extended symmetry groups, which may be small (finite) or large extensions of the corresponding automorphism group; we show examples of each of these behaviors, which come from real and imaginary quadratic number fields.

Posted on Oct 30, 2020 in Dynamical Systems, Seminars