An equidistribution theorem for biraitonal maps of ${\mathbb{P}}^k$

Abstract

We prove an equidistribution theorem of positive closed currents for a certain class of birational maps $f_{+}:{\mathbb{P}}^k\to {\mathbb{P}}^k$ of algebraic degree $d\ge 2$ satisfying ${\bigcup }_{n\ge 0}{f}_{-}^n(I^{+})\cap {\bigcup }_{n\ge 0}{f}_{+}^n(I^{-})=\varnothing$, where $f_{-}$ is the inverse of $f_{+}$ and $I^{\pm }$ are the sets of indeterminacy for $f_{\pm }$, respectively.

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References in corpus (1)

• Super-potentials, densities of currents and number of periodic points for holomorphic maps