2024/12/12 by Tristán Radić, Radić, Tristán
Computer Science · Engineering · Materials Science · #Cellular Automata and Applications #Advanced Materials and Mechanics #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2412.08884
Partial rigidity is a quantitative notion of recurrence and provides a global obstruction which prevents the system from being strongly mixing. A dynamical system (X, X, μ, T) is partially rigid if there is a constant δ>0 and sequence (nk)k ∈ ℕ such that \liminfk → ∞ μ(A ∩ TnkA) ≥ δμ(A) for every A ∈ X, and the partial rigidity rate is the largest δ achieved over all sequences. For every integer d ≥ 1, via an explicit construction, we prove the existence of a minimal subshift (X,S) with d ergodic measures having distinct partial rigidity rates. The systems built are S-adic subshifts of finite alphabetic rank that have non-superlinear word complexity and, in particular, have zero entropy.