IUMJ

Title: Speed of convergence towards attracting sets for endomorphisms of P^k

Authors: Johan Taflin

Issue: Volume 62 (2013), Issue 1, 33-44

Abstract:

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.