A. Banyaga, R. de la Llave, C. E. Wayne Cohomology equations near hyperbolic points and geometric versions of Sternberg linearization theorem. (100K, Plain TeX) ABSTRACT. We prove that if two germs of diffeomorphisms preserving a volume, symplectic or contact structure are tangent to a high enough order and the linearization is hyperbolic, it is possible to find a smooth change of variables preserving the same structure that sends one into the other. This result is a geometric version of Sternberg's linearization theorem which we recover as a particular case. An analogous result is also proved for flows.