Pinned Repetitions in Symbolic Flows: Preliminary Results

Fix some finite alphabet A and consider the compact space A of two-sided sequences over this alphabet. Here we endow A with the discrete topology and A with the product topology. We want to study repetitions in sequences ω ∈ A that either begin at the origin or are centered at the origin and hence are “pinned.” Moreover, we also want to study how many times arbitrarily long subwords are repeated in this way. Thus, for ω ∈ A, we define