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.  2006 Elsevier Inc. All rights reserved.