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

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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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Acknowledgments

The author thanks the referee for a very careful scrutiny and invaluable comments. This research was partially supported by JSPS Grant-in-Aid for Young Scientists (B), 24740087.

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  1. Division of Mathematics, Kyoto Institute of Technology, Sakyo-ku, Kyoto, 606-8585, Japan

    Yûsuke Okuyama

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  1. Yûsuke Okuyama
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Okuyama, Y. Quantitative approximations of the Lyapunov exponent of a rational function over valued fields. Math. Z. 280, 691–706 (2015). https://doi.org/10.1007/s00209-015-1443-6

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  • DOI: https://doi.org/10.1007/s00209-015-1443-6

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