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C. Favre, Mattias Jonsson (2002)
The Valuative Tree
The Lipschitz constant of a non-Archimedean rational function
T Chinburg, R Rumely (1993)
The capacity pairingJ. Reine Agnew. Math., 434
M. Baker, R. Rumely (2010)
Potential Theory and Dynamics on the Berkovich Projective Line
C. Favre, J. Rivera-Letelier (2007)
Théorie ergodique des fractions rationnelles sur un corps ultramétriqueProceedings of the London Mathematical Society, 100
J. Silverman (2007)
The Arithmetic of Dynamical Systems
(2013)
Topology and geometry of the Berkovich ramification locus I
T. Chinburg, R. Rumely (1993)
The capacity pairing.Journal für die reine und angewandte Mathematik (Crelles Journal), 1993
C. Favre, J. Rivera-Letelier (2004)
Théorème d'équidistribution de Brolin en dynamique p-adiqueComptes Rendus Mathematique, 339
F. Przytycki (1993)
Lyapunov characteristic exponents are nonnegative, 119
V. Berkovich (1990)
Spectral Theory and Analytic Geometry over Non-Archimedean Fields
Y. Okuyama (2013)
Quantitative approximations of the Lyapunov exponent of a rational function over valued fieldsMathematische Zeitschrift, 280
Y. Okuyama (2011)
Repelling periodic points and logarithmic equidistribution in non-archimedean dynamicsarXiv: Dynamical Systems
(2017)
An equidistribution result for dynamical systems onP1K
J. Doyle, Kenneth Jacobs, R. Rumely (2015)
Configuration of the crucial set for a quadratic rational mapResearch in Number Theory, 2
R. Rumely (2013)
The Minimal Resultant LocusarXiv: Dynamical Systems
(2017)
A new equivariant in non-Archimedean dynamics
Amaury Thuillier (2005)
Théorie du potentiel sur les courbes en géométrie analytique non archimédienne. Applications à la théorie d'Arakelov
J. Rivera-Letelier (2000)
Dynamique des fonctions rationelles sur des corps locaux
J. Rivera-Letelier (2005)
Points périodiques des fonctions rationnelles dans l'espace hyperbolique $p$-adiqueCommentarii Mathematici Helvetici, 80
Let K be an algebraically closed field of characteristic 0 that is complete with respect to a non-Archimedean absolute value, and let $$\phi \in K(z)$$ ϕ ∈ K ( z ) with $$\deg (\phi )\ge 2$$ deg ( ϕ ) ≥ 2 . Recently, Rumely introduced a family of discrete probability measures $$\{\nu _{\phi ^n}\}$$ { ν ϕ n } on the Berkovich line $$\mathbf{P }^1_{\text {K}}$$ P K 1 over K which carry information about the reduction of conjugates of $$\phi $$ ϕ . In a previous article, the author showed that the measures $$\nu _{\phi ^n}$$ ν ϕ n converge weakly to the canonical measure $$\mu _\phi $$ μ ϕ . In this article, we extend this result to allow test functions which may have logarithmic singularities at the boundary of $$\mathbf{P }^1_{\text {K}}$$ P K 1 . These integrands play a key role in potential theory, and we apply our main results to show the potential functions attached to $$\nu _{\phi ^n}$$ ν ϕ n converge to the potential function attached to $$\mu _\phi $$ μ ϕ , as well as an approximation result for the Lyapunov exponent of $$\phi $$ ϕ .
Research in Number Theory – Springer Journals
Published: Feb 8, 2018
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