Abstract
We study the dynamics of rational mappings f of C k by compactifying them in multiprojective spaces P n1 P ns. We focus on maps of the surface P 1 P 1 . We follow the ap- proach of (Si 99) and associate to any algebraically stablef an in- variant positive closedN1; 1O current. We then consider the exis- tence of anf invariant measure using the theory of pluripositive currents, and relates it to the measure of Russsakovskii-ShiVman describing the distribution of preimages of points. Our point of view enables us to treat new classes of examples: we consider in particular polynomial skew products with varying degrees, and birational polynomial mappings ofC 2 . We also describe the com- pact convex set off invariant currents for monomial and bira- tional maps of C 2 .
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