Is anything known about minimum dilatation pseudo-anosovs on non-orientable surfaces?


More specifically it is known whether the asymptotic behavior for log(minimal dilatation) is 1/genus? (The lower bound follows from the lower bound for pseudo-anosovs on orientable surfaces, but I do not know of any construction that realizes it.)



Minimum dilatation pseudo-anosovs on non-orientable surfaces
One may construct upper bounds in the non-orientable case the same way as McMullen does [in his paper](http://www.ams.org/mathscinet-getitem?mr=1832823) (see p. 523 for a short description of his "renormalization" procedure, or Section 10). 


