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Dynamics of regular birational maps in $$\mathbb P^k$$. (English) Zbl 1067.37055
Summary: We study some spaces of currents of bidegree $$(p,p)$$. As an application, we construct the equilibrium measure for a large class of birational maps of $$\mathbb P^k$$, as intersection of Green currents. We show that these currents are extremal and that the corresponding measure is mixing.

##### MSC:
 37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets 32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables 37A25 Ergodicity, mixing, rates of mixing 32U40 Currents
##### Keywords:
Birational map; Green current; Mixing measure
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##### References:
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