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Orbits of complete families of vector fields on a subcartesian space are shown to be
smooth manifolds. This allows a description of the structure of the reduced phase space
of a Hamiltonian system in terms of the reduced Poisson algebra. Moreover, one can give a
global description of smooth geometric structures on a family of manifolds, which form a
singular foliation of a subcartesian space, in terms of objects defined on the
corresponding family of vector fields. Stratified...
We consider the following problem: find on a plurisubharmonic function with a given order function. In particular, we prove that any positive ambiguous function on which is constant outside a polar set is the order function of a plurisubharmonic function.
Nous étudions les espaces analytiques rigides de dimension 1, réguliers, de genre fini sur un corps valué complet . Nous montrons qu’un tel espace admet une réduction préstable. Si est maximalement complet, se plonge dans une courbe algébrique (analytifiée). On donne aussi une caractérisation des espaces analytiques qui sont le complémentaire d’une partie compacte dans une courbe algébrique.
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