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Géométrie, points entiers et courbes entières

Pascal Autissier (2009)

Annales scientifiques de l'École Normale Supérieure

Soit X une variété projective sur un corps de nombres K (resp. sur ). Soit H la somme de « suffisamment de diviseurs positifs » sur X . On montre que tout ensemble de points quasi-entiers (resp. toute courbe entière) dans X - H est non Zariski-dense.

Geometry and dynamics of admissible metrics in measure spaces

Anatoly Vershik, Pavel Zatitskiy, Fedor Petrov (2013)

Open Mathematics

We study a wide class of metrics in a Lebesgue space, namely the class of so-called admissible metrics. We consider the cone of admissible metrics, introduce a special norm in it, prove compactness criteria, define the ɛ-entropy of a measure space with an admissible metric, etc. These notions and related results are applied to the theory of transformations with invariant measure; namely, we study the asymptotic properties of orbits in the cone of admissible metrics with respect to a given transformation...

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