Pseudo-Anosov homeomorphisms of punctured non-orientable surfaces with small stretch factor

Abstract

We prove that in the non-orientable setting, the minimal stretch factor of a pseudo-Anosov homeomorphism of a surface of genus $g$ with a fixed number of punctures is asymptotically on the order of $\frac{1}{g}$. Our result adapts the work of Yazdi to non-orientable surfaces. We include the details of Thurston's theory of fibered faces for non-orientable 3-manifolds.