Th\'eor\`emes de Borel avec contraintes

TL;DR

This paper explores Borel's theorem in the context of Lie algebras of vector fields and groups of diffeomorphisms, extending classical results to more complex geometric structures.

Contribution

It generalizes Borel's theorem to Lie algebras of vector fields and diffeomorphism groups, incorporating constraints in these geometric settings.

Findings

Extension of Borel's theorem to Lie algebras of vector fields

Application to groups of diffeomorphisms

New methods for handling constraints in geometric contexts

Abstract

A classical theorem due to Borel asserts that any formal serie with real coefficients is the Taylor expansion of a germ of $\mathcal{C}^{\infty}- {\rm function}$. We study such a problem in the context of Lie algebras of vector fields or of groups of diffeomorphisms.