The complexity of a minimal sub-shift on symbolic spaces

Let (Σ,ρ) be a one-sided symbolic space (with two symbols), and let σ be the shift on Σ. In this paper, we prove that there exists a minimal set T⊂Σ such that σ|T is Wiggins chaotic, Martelli chaotic, distributionally chaotic, strictly ergodic, topologically weakly mixing and has zero topological entropy.