There has been a great deal of recent research in multivariable complex dynamics, most of it devoted to either polynomial diffeomorphisms of C2 or holomorphic maps of Pn . Pluripotential theory plays a prominent supporting role in nearly all this work. Our concern in this paper and its predecessor [Dil] is to extend the ap- plication of pluripotential theory to study dynamics of birational maps of P2 . Anyone who seeks to understand the dynamics of a birational map f+ : P2 -> P2 faces an immediate problem birational maps are not generally maps. That is, except when f+ has degree d = l, there exists a finite non-empty set 1+ of points where f+ cannot be defined continuously. In a precise sense, f+ ``blows up'' each of these points of indeterminacy to an entire algebraic curve. Nevertheless, we be- lieve that it is worthwhile to pretend as far as possible that birational maps really are diffeomorphisms .
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