Mixing properties in expanding Lorenz maps

Let T _f:[0,1]→[0,1] be an expanding Lorenz map, this means T _fx:=f(x)(mod 1) where f:[0,1]→[0,2] is a strictly increasing map satisfying inf⁡f ^′>1. Then T _f has two pieces of monotonicity. In this paper, sufficient conditions when T _f 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 T _f being locally eventually onto are considered, and some gaps in classical results on the dynamics of Lorenz maps are corrected.