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

2011/10/25 by Taflin, Johan
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1110.5569

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 τ, 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 fⁿ converge to τexponentially fast. We also prove that the equilibrium measure on A is hyperbolic.

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