Equidistribution speed for polynomial-like maps

Let $f$ be a polynomial-like map of large topological degree. By Dinh-Sibony’s result, the measures $d_t^{-n}(f^n)^*\delta_a$ converge to the Green measure of $f$. This result is valid for a generic point $a$ and includes a controlled error bound depending on $a$. In this talk, we examine the rate at which this convergence occurs.