A generalization of Ostrowski' theorem on ultrametric inequalities.
A p-adic behaviour of dynamical systems.
We study dynamical systems in the non-Archimedean number fields (i.e. fields with non-Archimedean valuation). The main results are obtained for the fields of p-adic numbers and complex p-adic numbers. Already the simplest p-adic dynamical systems have a very rich structure. There exist attractors, Siegel disks and cycles. There also appear new structures such as fuzzy cycles. A prime number p plays the role of parameter of a dynamical system. The behavior of the iterations depends on this parameter...
A spectral theorem for matrices over fields of power series
About -adic interpolation of continuous and differentiable functions
Absolute values on algebras
Amibes de variétés algébriques et dénombrement de courbes
Les amibesdes variétés algébriques dans sont les images de ces variétés par l’application des moments , . Des résultats obtenus par G. Mikhalkin montrent l’utilité des amibes pour l’étude des variétés algébriques réelles et complexes. Les amibes peuvent être déformées en des complexes polyédraux appelésvariétés algébriques tropicales. Cette déformation permet, en particulier, de calculer les invariants de Gromov-Witten du plan projectif et d’autres surfaces toriques en dénombrant des courbes...
An Algorithm for Lifting Points in a Tropical Variety
An application of newton iteration procedure to -adic differential equations
An ultrametric Nevanlinna’s second main theorem for small functions of a special type
In ultrametric Nevanlinna theory, the Nevanlinna’s second main theorem for small functions has only been proved in the case of at most three small functions. In this paper, we prove a second main theorem for small functions of a special type when the residue characteristic of the field is zero.
Analyse -adique
Analytic functions on an open subsets of P1 (k).
Automorphismes et dérivations de «petites normes» sur un corps value non archimédien