Quantitative approximations of the Lyapunov exponent of a rational function over valued fields

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 $0$ 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.

17 pages. Theorem 1 is improved

References in corpus (3)

• Repelling periodic points and logarithmic equidistribution in non-archimedean dynamics
• Adelic equidistribution, characterization of equidistribution, and a general equidistribution theorem in non-archimedean dynamics
• Fekete configuration, quantitative equidistribution and wandering critical orbits in non-archimedean dynamics

Cited by in corpus (2)

• Continuity of the Green function in meromorphic families of polynomials
• On a characterization of polynomials among rational functions in non-archimedean dynamics