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Enveloppe galoisienne d'une application rationnelle de P1.

Guy Casale (2006)

Publicacions Matemàtiques

In 2001, B. Malgrange defines the D-envelope or galoisian envelope of an analytical dynamical system. Roughly speaking, this is the algebraic hull of the dynamical system. In this short article, the D-envelope of a rational map R: P1 --> P1 is computed. The rational maps characterised by a finitness property of their D-envelope appear to be the integrable ones.

Existence of star-products on exact symplectic manifolds

Marc De Wilde, P. B. A. Lecomte (1985)

Annales de l'institut Fourier

It is shown that if a manifold admits an exact symplectic form, then its Poisson Lie algebra has non trivial formal deformations and the manifold admits star-products. The non-formal derivations of the star-products and the deformations of the Poisson Lie algebra of an arbitrary symplectic manifold are studied.

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