  A symmetric Lorenz map is obtain by ``flipping'' one of the two branches of a
symmetric unimodal map. We use this to derive a Sharkovsky-like theorem for
symmetric Lorenz maps, and also to find cases where the unimodal map restricted
to the critical omega-limit set is conjugate to a Sturmian shift. This has
connections with properties of unimodal inverse limit spaces embedded as
attractors of some planar homeomorphisms.
