Yûsuke Okuyama
Published 2013-09-10, updated 2014-10-05Version 3
We establish a quantitative approximation formula of the Lyapunov exponent of a rational function of degree more than one over an algebraically closed field of characteristic $0$ that is complete with respect to a non-trivial and possibly non-archimedean absolute value, in terms of the multipliers of periodic points of the rational function. This quantifies both our former convergence result over general fields and the one-dimensional version of Berteloot--Dupont--Molino's one over archimedean fields.
Comments: 17 pages. Theorem 1 is improved
On symmetries of iterates of rational functions
On the spherical derivative of a rational function
Rational functions with real multipliers
![QR code for arXiv:1309.2479 [math.DS]](http://oss.arxitics.com/images/favicon.svg)