Uniquely ergodic subshifts over compactifications of the naturals

RESUMEN: In this talk, we will discuss one-dimensional substitution subshifts over (infinite) compact alphabets and their dynamical properties. As a motivating class, we will focus on shifts generated by a parametrised family of substitutions on certain compactifications of the natural numbers. We will provide a general checkable condition for unique ergodicity that relies on compactness properties of the substitution operator, which the analogue of the substitution matrix for infinite alphabets.

Posted on Jan 8, 2024 in Dynamical Systems, Seminars