Equidistribution of the crucial measures in non-Archimedean dynamics

Text. Let K be a complete, algebraically closed, non-Archimedean valued field, and let phi is an element of K(z) with deg(phi) >= 2. In this paper we consider the family of functions ord Res(phi n)(x), which measure the resultant of phi(n) at points x in P-k(1), the Berkovich projective line, and show that they converge locally uniformly to the diagonal values of the Arakelov-Green's function g mu(phi)(x, x) attached to the canonical measure of phi. Following this, we are able to prove an equidistribution result for Rumely's crucial measures nu(phi n), each of which is a probability measure supported at finitely many points whose weights are determined by dynamical properties of phi. Video. For a video summary of this paper, please visit https://youtu.be/YCCZDliwe00.(C) 2017 Elsevier Inc. All rights reserved.