Continuous Families of Rational Surface Automorphisms with Positive   Entropy
  We construct k-parameter families of rational surface automorphisms for any k. These are automorphisms of surfaces X, which are constructed from iterated blowups over the projective plane. In certain cases: we are able to determine the exact automorphism group of X, as well as when two of the surfaces X are inequivalent. 
Eric Bedford and Kyounghee Kim