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

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

2011-10-25

arxiv.org/abs/1110.5569v2

Mathematics

Dynamical Systems

Scientific paper

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.

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