Topological transitivity for expanding piecewise monotonic maps on the interval

Let T : [0, 1] → [0, 1] be an expanding piecewise monotonie map. Conditions on T and infx∈[0,1] |T′x| implying the topological transitivity of T are investigated. For a monotonic mod one transformation T topological transitivity is obtained, if inf x∈[0, 1] |T′x| > 2. If T is a monotonic mod one transformation with three monotonic pieces, then infx∈[0,1] |T′x| ≥ 2 implies the topological transitivity of T. An expanding monotonic mod one transformation T with limx→0+ Tx = 0 or limx→1- Tx = 1 is topologically transitive. © Birkhäuser Verlag, Basel, 1999.