Complexity of a kind of interval continuous self-map of finite type

► We find the Hausdorff dimension for an interval continuous self-map f of finite type is s∈(0,1) on a non-wandering set. ► f|Ω(f) has positive topological entropy. ► f|Ω(f) is chaotic such as Devaney chaos, Kato chaos, two point distributional chaos and so on.