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For any k we construct k-parameter families of rational surface automorphisms with positive entropy. These are automorphisms of surfaces $${\mathcal{X}}$$, which are constructed from iterated blowups over the projective plane. In certain cases we are able to determine the exact automorphism group of $${\mathcal{X}}$$, as well as when two of these surfaces are inequivalent.

Continuous families of rational surface automorphisms with positive entropy