Abstract
We give a theorem of characterization for the property of being topologically equivalent after blow-up in the set of germs of three-dimensional hyperbolic vector fields. Given ξ, ξ ′ two such a germs and Φ a finite sequence of blow-ups of the ambient space, we find, under non-resonance conditions associated to Φ, a criterion that permits to determine if there is a topological equivalence between ξ and ξ ′ that lifts to Φ. We deduce that there are only finitely many possible classes of Φ-topological equivalence in the considered set of vector fields.
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