  Dilation surfaces, or twisted quadratic differentials, are variants of
translation surfaces. In this paper, we study the question of what elements or
subgroups of the mapping class group can be realized as affine automorphisms of
dilation surfaces. We show that dilation surfaces can have exotic Dehn twists
in their affine automorphism groups and will establish that only certain types
of mapping class group elements can arise as affine automorphisms of dilation
surfaces. We also generalize a construction of Thurston that constructs a
translation surface from a pair of filling multicurves to dilation surfaces.
This construction will give us dilation surfaces that realize a pair of Dehn
multitwists in their affine automorphism groups.
