Premium
Equidistribution and Nevanlinna theory
Author(s) -
Drasin David,
Okuyama Yûsuke
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm054
Subject(s) - mathematics , nevanlinna theory , pure mathematics , mathematical economics , algebra over a field , calculus (dental) , meromorphic function , medicine , dentistry
Russakovskii and Shiffman quantified the equidistribution theorem of Brolin, Lyubich and Freire–Lopes–Mañé by showing that the (normalized) measures determined by counting preimages of a point a ∈ ℂ converge exponentially to the equilibrium measure independent of a with the exception of a polar set. By intertwining classical Nevanlinna‐theoretic arguments with complex dynamics, we identify Russakovskii and Shiffman's exceptional set (in the situation of one complex variable) as the finite set of all superattracting periodic points, and also present a sharper estimate of the rate of convergence to the equilibrium measure. This yields statistical properties of rational maps.