Quantitative approximations of the Lyapunov exponent of a rational function over valued fields
Dynamical Systems
2017-05-17 v3 Complex Variables
Number Theory
Abstract
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 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.
Keywords
Cite
@article{arxiv.1309.2479,
title = {Quantitative approximations of the Lyapunov exponent of a rational function over valued fields},
author = {Yûsuke Okuyama},
journal= {arXiv preprint arXiv:1309.2479},
year = {2017}
}
Comments
17 pages. Theorem 1 is improved