Speed of convergence towards attracting sets for endomorphisms of P^k Johan Taflin ?Complex dynamicsattractorcurrentq-convex set Let $f$ be a non-invertible holomorphic endomorphism of $\mathbb{P}^k$ having an attracting set $A$. We show that, under some natural assumptions, $A$ supports a unique invariant positive closed current $\tau$, of the right bidegree and of mass $1$. Moreover, if $R$ is a current supported in a small neighborhood of $A$, then its push-forwards by $f^n$ converge to $\tau$ exponentially fast. We also prove that the equilibrium measure on $A$ is hyperbolic. Indiana University Mathematics Journal 2013 text pdf 10.1512/iumj.2013.62.4895 10.1512/iumj.2013.62.4895 en Indiana Univ. Math. J. 62 (2013) 33 - 44 state-of-the-art mathematics http://iumj.org/access/