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 $d\geq 2$ satisfying $\bigcup_{n\geq 0}f_-^n(I^+)\cap \bigcup_{n\geq 0}f_+^n(I^-)=\emptyset$, where $f_-$ is the inverse of $f_+$ and $I^\pm$ are the sets of indeterminacy for $f_\pm$, respectively.