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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.

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
Full Text: DOI arXiv
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