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Laminar currents in \(\mathbb P^2\). (English) Zbl 1021.37018
Summary: We study laminar currents in \(\mathbb P^2\). Given a sequence of irreducible algebraic curves \((C_n)\) converging in the sense of currents to \(T\), we find geometric conditions on the curves ensuring that the limit current \(T\) is laminar. This criterion is then applied to meromorphic dynamical systems in \(\mathbb P^2\), and laminarity of the dynamical “Green” current is obtained for a wide class of meromorphic self maps of \(\mathbb P^2\), as well as for all bimeromorphic maps of projective surfaces.

MSC:
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
32U40 Currents
32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables
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