Mixing properties in expanding Lorenz maps

Let Tf:[0,1]→[0,1] be an expanding Lorenz map, this means Tfx:=f(x)(mod 1) where f:[0,1]→[0,2] is a strictly increasing map satisfying inf⁡f′>1. Then Tf has two pieces of monotonicity. In this paper, sufficient conditions when Tf is topologically mixing are provided. For the special case f(x)=βx+α with β≥23 a full characterization of parameters (β,α) leading to mixing is given. Furthermore relations between renormalizability and Tf being locally eventually onto are considered, and some gaps in classical results on the dynamics of Lorenz maps are corrected.