Speed of convergence towards attracting sets for endomorphisms of P^k
Dynamical Systems
2012-02-15 v2 Complex Variables
Abstract
Let f be a non-invertible holomorphic endomorphism of 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.
Keywords
Cite
@article{arxiv.1110.5569,
title = {Speed of convergence towards attracting sets for endomorphisms of P^k},
author = {Johan Taflin},
journal= {arXiv preprint arXiv:1110.5569},
year = {2012}
}