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arXiv · 1309.2479

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

Yûsuke Okuyama
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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.

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Yûsuke Okuyama. 2014-10-05. Quantitative approximations of the Lyapunov exponent of a rational function over valued fields. https://doi.org/10.1007/s00209-015-1443-6

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