Abstract
We consider dimension 3 vector fields (resp. diffeomorphisms), in a neighborhood of a hyperbolic saddle. We give a criterion to decide if the imaginary part (resp. the angular part) of the eigenvalues of the linear part of the dynamical system at the fixed point is a topological conjugacy invariant if we assume that the conjugacy maps a non-spiraling curve onto another one. We apply this result to the situation of diffeomorphisms and vector fields with a quasi-transversal homoclinic orbit. To cite this article: E. Dufraine, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 53–58
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