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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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