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Displaying similar documents to “Dynamique des polynômes quadratiques sur les corps locaux”

Mesures invariantes pour les fractions rationnelles géométriquement finies

Guillaume Havard (1999)

Fundamenta Mathematicae

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Let T be a geometrically finite rational map, p(T) its petal number and δ the Hausdorff dimension of its Julia set. We give a construction of the σ-finite and T-invariant measure equivalent to the δ-conformal measure. We prove that this measure is finite if and only if p ( T ) + 1 p ( T ) δ > 2 . Under this assumption and if T is parabolic, we prove that the only equilibrium states are convex combinations of the T-invariant probability and δ-masses at parabolic cycles.

Minoration de la hauteur normalisée des hypersurfaces

Francesco Amoroso, Sinnou David (2000)

Acta Arithmetica

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1. Introduction. Dans un article célèbre, D. H. Lehmer posait la question suivante (voir [Le], §13, page 476): «The following problem arises immediately. If ε is a positive quantity, to find a polynomial of the form: f ( x ) = x r + a 1 x r - 1 + ⋯ + a r where the a’s are integers, such that the absolute value of the product of those roots of f which lie outside the unit circle, lies between 1 and 1 + ε (...). Whether or not the problem has a solution for ε < 0.176 we do not know.» Cette question, toujours ouverte,...