Benalili, Mohammed2013-05-162013-05-162011-010393-0440https://dspace.univ-tlemcen.dz/handle/112/1900Journal of Geometry and Physics, ISSN : 0393-0440, DOI : 10.1016/j.geomphys.2010.08.009, Issue : 1, Volume : 61, pp. 62–76, January 2011.In the first part of this paper we give suitable spectral properties of the adjoint operators induced by appropriate perturbations of some hyperbolic linear vector fields. These properties are useful to prove general facts based on the Nash–Moser inverse function theorem. In the second part of this work we study circumstances where a global linearization of a vector field X in a real numerical space is feasible and where some diffeomorphisms which are close to exp(X) can be embedded in a flow.enExponential mapCategory of tame Fréchet manifoldsNash–Moser function inverse theoremArticle