Topological transitivity for expanding piecewise monotonic maps on the interval

Summary.

Let T : [0, 1] → [0, 1] be an expanding piecewise monotonic map. Conditions on T and ${\rm inf}_{x\in [0,1]}|T^{\prime}x|$ implying the topological transitivity of T are investigated. For a monotonic mod one transformation T topological transitivity is obtained, if ${\rm inf}_{x\in [0,1]}|T^{\prime}x| > 2$. If T is a monotonic mod one transformation with three monotonic pieces, then ${\rm inf}_{x\in [0,1]}|T^{\prime}x| \geq 2$ implies the topological transitivity of T. An expanding monotonic mod one transformation T with lim _{x → 0}+ T x = 0 or lim _{x → 1} - T x = 1 is topologically transitive.