Topological transitivity for expanding monotonic mod one transformations with two monotonic pieces - Raith, Peter (Annales Mathematicae Silesianae, 1999)
Consider a continuous and strictly increasing function f: [0,1]→[0,2], and define Tfx = f(x)(mod 1). Then Tf is a monotonie mod one transformation with two monotonic pieces, if and only if f(0) < 1 < f(1). It is proved that Tf is topologically transitive, if f is piecewise differentiable and infx∈[0,1]f'(x) ≥ √2.