2022/06/20 by Creutz, Darren
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2206.10047
We resolve a long-standing open question on the relationship between measure-theoretic dynamical complexity and symbolic complexity by establishing the exact word complexity at which measure-theoretic strong mixing manifests: For every superlinear f : ℕ → ℕ, i.e. f(q)/q → ∞, there exists a subshift admitting a (strongly) mixing of all orders probability measure with word complexity p such that p(q)/f(q) → 0. For a subshift with word complexity p which is non-superlinear, i.e. \liminf p(q)/q < ∞, every ergodic probability measure is partially rigid.