Mixing properties in expanding Lorenz maps.

Abstract Let T f : [ 0 , 1 ] → [ 0 , 1 ] be an expanding Lorenz map, this means T f x : = 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) = β x + α with β ≥ 2 3 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. [ABSTRACT FROM AUTHOR]